The Quran

وَعَدَ اللَّهُ الَّذينَ آمَنوا مِنكُم وَعَمِلُوا الصّالِحاتِ لَيَستَخلِفَنَّهُم فِي الأَرضِ كَمَا استَخلَفَ الَّذينَ مِن قَبلِهِم وَلَيُمَكِّنَنَّ لَهُم دينَهُمُ الَّذِي ارتَضىٰ لَهُم وَلَيُبَدِّلَنَّهُم مِن بَعدِ خَوفِهِم أَمنًا ۚ يَعبُدونَني لا يُشرِكونَ بي شَيئًا ۚ وَمَن كَفَرَ بَعدَ ذٰلِكَ فَأُولٰئِكَ هُمُ الفاسِقونَ

Muhammad Asad

God has promised those of you who have attained to faith and do righteous deeds that, of a certainty, He will cause them to accede to power on earth,¹ even as He caused [some of] those who lived before them to accede to it; and that, of a certainty, He will firmly establish for' them the religion which He has been pleased to bestow on them;² and that, of a certainty, He will cause their erstwhile state of fear to be replaced by a sense of security³ - [seeing that] they worship Me [alone], not ascribing divine powers to aught beside Me.⁴ But all who, after [having understood] this, choose to deny the truth - it is they, they who are truly iniquitous!

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.
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.
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.)
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.