These verses were revealed in Madinah (Mawdudi and Dr. Muhammad Asad).
24:53 And they swear by Allah their strongest oaths that if you ordered them, they would go forth [in Allah’s cause]. Say, “Do not swear. [Such] obedience is known. Indeed, Allah is Acquainted with that which you do.”
24:55 Allah has promised those who have believed among you and done righteous deeds that He will surely grant them succession [to authority] upon the earth just as He granted it to those before them and that He will surely establish for them [therein] their religion which He has preferred for them and that He will surely substitute for them, after their fear, security, [for] they worship Me, not associating anything with Me. But whoever disbelieves after that – then those are the defiantly disobedient.
24:53 – The verse is directed at those hypocrites in the life-time of Prophet Muhammed (p), who would swear an oath that they would be there helping the Muslims no matter what situation. In reality, they were double-faced liars, who would back-stab the Muslims and side with an enemy against the believers (Tafsir Ibn kathir and Tafsir Jalalayn).
24:55 – God Almighty in this verse promised the believers who done righteous deeds that HE will grant them success on earth. This promise was indeed given and HE did give victory and success before the demise of Prophet Muhammed (p). And made Islam prevail in Arabia through preaching.
Dr. Muhammad Asad:
“69 This is an allusion to the ephemeral, self-deceiving enthusiasms of the half-hearted and their supposed readiness for “self-sacrifice”, contrasting with their obvious reluctance to live up to the message of the Qur’an in their day-to-day concerns.
70 This elliptic phrase alludes to the principle – repeatedly stressed in the Qur’an – that God does not burden man with more than he can easily bear.
71 Lit., “cause them to be successors on earth” – i.e., enable them to achieve, in their turn, power and security and, thus, the capability to satisfy their worldly needs. This Qur’anic reference to God’s “promise” contains an oblique allusion to the God-willed natural law which invariably makes the rise and fall of nations dependent on their moral qualities.
72 Cf. 5:3 – “I have willed that self-surrender unto Me (al-islam) shall be your religion”. Its “firm establishment” (tamkin) relates to the strengthening of the believers’ faith as well as to the growth of its moral influence in the world.
73 Lit., “exchange for them, after their fear [or “danger”], security”. It is to be noted that the term amn signifies not merely outward, physical security but also – and, indeed, originally – “freedom from fear” (Taj al-‘Arus). Hence, the above clause implies not only a promise of communal security after an initial period of weakness and danger (which, as history tells us, overshadows the beginnings of every genuine religious movement), but also the promise of an individual sense of inner security – that absence of all fear of the Unknown which characterizes a true believer. (See next note.)
74 I.e., the believer’s freedom from fear is a direct outcome of his intellectual and emotional refusal to attribute to anyone or anything but God the power to shape his destiny.” 
Maulana Muhammad Ali:
“55a. This verse not only prophesies the establishment of the kingdom of Islam, but also its permanence, so that successors will be raised to the Holy Prophet and the Muslims made a ruling nation on earth. By those before them are meant in particular the followers of Moses (Bd). Islam at the time of the revelation of these verses was still surrounded by enemies on all sides; there was still fear for the believers, as the verse clearly shows, and idol-worship still had the upper hand in Arabia. The triumph of Islam, which is prophesied in the parable of the Divine Light first, and the gradual advent of which is referred to afterwards, is here predicted in the clearest and most emphatic terms: the believers will be made rulers in the earth; their religion will be firmly established; security will be given to them in place of fear; Divine Unity will rule supreme. All these favours will be bestowed upon the Muslims, for which they should be thankful; but, if they are ungrateful after that, they shall be dealt with as transgressors. Kafara means he disbelieved as well as he was ungrateful, and the latter significance suits the context here. Even if kufr is taken as meaning disbelief here, it would mean a denial in practice, or disobedience to Divine commandments.” 
Background on verse 55.
Mufti Muhammed Usmani Shafi:
“BACKGROUND OF REVELATION
“Qurtubi has reported on authority of Abul Aliyah that the Holy Prophet stayed in Makkah for ten years after commencement of revelation and declaration of Prophet-hood, during which time there was constant fear of the disbelievers. Then after the Hijrah to Madinah also there was a ceaseless danger of attacks from the disbelievers. So, someone asked the Holy Prophet, ‘Would a time come to us when we will be able to live in peace without wearing our weaponry?’ The Holy Prophet replied, ‘Yes, the time is coming very soon’. On that occasion these verses were revealed. (Qurtubi and Bahr). Sayyidina Abdullah Ibn Abbas has said that these verses relate the promise of Allah Ta’ala which He had made with the Ummah of Muhammad before their creation in the Torah and the Injil. (Bahr Muhit).” 
Shaykh Muhammed Ashiq Ilahi Madni:
“THE FALSE OATHS OF THE HYPOCRITES TO BE OBEDIENT
Referring to the hypocrites, Allah says,
‘They swear solemn oaths in Allah’s name, saying that if you command them they will certainly leave their homes.’ This is the interpretation of Abdullah bin Abbas (ra). Other commentators’ say that the oath refers to marching in Jihad. Allah says,
‘Tell them, ‘Do not swear. Obedience can be recognised.’
This means that a person does not have to take an oath when he sincere. Oaths betray a lack of sincerity and the hypocrites were certainly false in these oaths. The Muslims knew that they merely offered lip service and would never uphold their oaths. Their true colours will be exposed on the inevitable Day of Judgement because ‘Allah is surely informed of what you do.’
‘Say (to the hypocrites), ‘Obey Alah and obey the Messenger. If they turn away, then the messenger (will suffer no loss because he) is responsible only for what he has been entrusted with (i.e., propagation) and you people are responsible for what you have been entrusted with (i.e., obedience and submission).’
‘If you obey, you will be rightly guided (if not, you will suffer the consequences). The Messenger is responsible only for clear propagation.’ The Holy Prophet (p) has fulfilled his task, leaving people to fulfil theirs. Like the holy Prophet (p), those after him are entrusted only with the same task and are not obliged to force people to respond.
THE PROMISE OF SOVEREIGNTY FOR THE BELIEVERS ON EARTH
‘Ma’alimut Tanzil’ (v. 3 p. 353) reports from Sayyidina Abul Aliya (ra) that the Holy Prophet (ra) remained steadfast with the Sahabah from the beginning of his the Prophethood. He endured untold sufferings at the hands of the Polytheists AND WAS FORCED TO MIGRATE TO MADINAH. EVEN THERE, THE MUSLIMS WERE STILL AT RISK BECAUSE, ADDED TO THE DANGER OF THE POLYTHEISTS, THE HYPOCRITES AND THE JEWS WERE ALSO ANTAGONISTIC TOWARDS THEM.
AS A RESULT, THEY WERE FORCED TO REMAIN ARMED AT ALL TIMES. This state of affairs caused someone to say,
‘When will the day dawn when we will be at peace and not require our weapons?’
In response to this, Allah revealed the above verse viz.
‘Allah has promised those of you who believe and do good deeds that He will definitely make them successors on earth just as He had made those before them successors.’
Allah promised them that the time was near when He would grant them sovereignty on earth as He gave to Dawud (David) (as), Sulayman (Solomon) and the many leaders of the Bani Isra’il (Children of Israel).
Sayyidina Musa (Moses) (as) once told the Bani Isra’il (Children of Israel),
‘O my people, remember Allah’s bounty on you when He raised messengers among you and made you kings. He gave you what He never gave anyone in the entire universe.’ [Surah Ma’idah (5), verse 20]
The realisation of Allah’s promise is based on belief (Iman) and righteous deeds. …
Allah promised further that He ‘will certainly grant strength to them in the religion (Din) that He has chosen for them and will certainly replace their fear with peace.’
The Muslims lived in perpetual dear while in Makkah, then again in Madinah. However, Allah soon alleviated their fears, thereby fulfilling His promise to them.
Allah then says, They worship Me and do not ascribe any as partner of Myself.’
They neither commit Shirl, nor do they carry out deeds for any other be sides Allah.” 
Tafsir Ibn Kathir:
“…(Have you not observed the hypocrites who say to their friends among the people of the Scripture who disbelieve: “If you are expelled, we indeed will go out with you, and we shall never obey any one against you; and if you are attacked, we shall indeed help you.” But Allah is Witness that they verily are liars. Surely, if they are expelled, never will they go out with them; and if they are attacked, they will never help them. And if they do help them, they will turn their backs, and they will not be victorious.) 59:11-12… (Tafsir Ibn Kathir – Online Source)
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 The Message of The Quran translated and explained by Muhammad Asad, page 768 – 769
 The Holy Quran Arabic Text with English Translation, Commentary and comprehensive Introduction by Maulana Muhammad Ali, page 712
 Maarif-ul Quran, by Mufti Muhammed Usmani Shafi, volume 6, page 451
 Illuminating Discourses on the Noble Quran – Tafseer Anwarul Bayan – By Shaykh Muhammed Ashiq Ilahi Muhajir Madni (r.a), volume 3, page 603 – 605