Qur’an verses about hope

۞ قُلْ يَٰعِبَادِىَ ٱلَّذِينَ أَسْرَفُوا۟ عَلَىٰٓ أَنفُسِهِمْ لَا تَقْنَطُوا۟ مِن رَّحْمَةِ ٱللَّهِ ۚ إِنَّ ٱللَّهَ يَغْفِرُ ٱلذُّنُوبَ جَمِيعًا ۚ إِنَّهُۥ هُوَ ٱلْغَفُورُ ٱلرَّحِيمُ

Say, "O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful."

Addressed to those who have transgressed against themselves: do not despair of the mercy of Allah, for He forgives all sins.

يَٰبَنِىَّ ٱذْهَبُوا۟ فَتَحَسَّسُوا۟ مِن يُوسُفَ وَأَخِيهِ وَلَا تَا۟يْـَٔسُوا۟ مِن رَّوْحِ ٱللَّهِ ۖ إِنَّهُۥ لَا يَا۟يْـَٔسُ مِن رَّوْحِ ٱللَّهِ إِلَّا ٱلْقَوْمُ ٱلْكَٰفِرُونَ

O my sons, go and find out about Joseph and his brother and despair not of relief from Allah. Indeed, no one despairs of relief from Allah except the disbelieving people."

Yaqub sends his sons to look for Yusuf and his brother: despair not of relief from Allah.

قَالَ وَمَن يَقْنَطُ مِن رَّحْمَةِ رَبِّهِۦٓ إِلَّا ٱلضَّآلُّونَ

He said, "And who despairs of the mercy of his Lord except for those astray?"

Ibrahim's words when told of a son in old age: who despairs of the mercy of his Lord except those astray?

إِنَّ ٱلَّذِينَ ءَامَنُوا۟ وَٱلَّذِينَ هَاجَرُوا۟ وَجَٰهَدُوا۟ فِى سَبِيلِ ٱللَّهِ أُو۟لَٰٓئِكَ يَرْجُونَ رَحْمَتَ ٱللَّهِ ۚ وَٱللَّهُ غَفُورٌۭ رَّحِيمٌۭ

Indeed, those who have believed and those who have emigrated and fought in the cause of Allah - those expect the mercy of Allah. And Allah is Forgiving and Merciful.

Those who believed, emigrated and strove in the cause of Allah are described as hoping for the mercy of Allah.

فَإِنَّ مَعَ ٱلْعُسْرِ يُسْرًا

For indeed, with hardship [will be] ease.

From Ash-Sharh: with hardship there will be ease, repeated in the next verse.