In Shemoneh Esrei, we see a direct relation between doing Teshuva and achieving Geula.
This corresponds to the Gemara (Yoma 86b), Rabbi Yochanan said: Great is teshuva because it brings the redemption, as it says, “A redeemer will come to Tzion, and to those of Ya’akov who repent from willful sin” (Yeshayahu 59:20-21).
The three brachot below, in the “bakasha” section of Shemoneh Esrei, begin with repentance and forgiveness and end with redemption.
I. Bakasha Section of Shemoneh Esrei
Cause us to return, our Father, to Your Torah; draw us near, our King, to Your service; and bring us back to You in whole-hearted repentance. Blessed are You L-rd, who desires penitence.
Pardon us, our Father, for we have sinned; forgive us, our King, for we have transgressed; for You are a good and forgiving G‑d. Blessed are You L-rd, gracious One who pardons abundantly.
O behold our affliction and wage our battle; redeem us speedily for the sake of Your Name, for You G‑d are the mighty redeemer. Blessed are You L-rd, Redeemer of Israel.