As stated, repentance is a Gift from the Saviour. Now to be more specific, how is it applied to them its given to as a Gift, namely Gods Elect ? Peter tells us here 1 Pet 1:3
Blessed be the God and Father of our Lord Jesus Christ, which according to his abundant mercy hath begotten us again unto a lively hope by the resurrection of Jesus Christ from the dead,
All for whom Christ died, by His Resurrection from the Dead, they shall be begotten again ! These words begotten again are in the greek anagennaó and means:
I beget again, beget into a new life.
to produce again, beget again, beget anew; metaphorically: τινα, thoroughly to change the mind of one, so that he lives a new life and one conformed to the will of God
Notice that it changes the mind of one, this being begotten again. Now what is repentance ? Its the greek word metanoia and means:
repentance, a change of mind, change in the inner man.
So this repentance that is given by and through the resurrection of Christ, being begotten again, effects a change of mind, which what primarily what repentance entails. It gives also change in the inner man.
And so repentance is confirmed to be the Gift of Christ through His resurrection from the dead, and its given to all for whom He died as their Saviour !