take heart

take heart (from sth) (start to feel more hopeful, more confident, and encouraged; receive courage or comfort from some fact) — не падать духом, мужаться, собраться с духом, осмелеть; не унывать

Example: Take heart! — Не падай духом! Не унывай! Мужайся!

Also {bookish}:
lift up one's heart
take heart of grace

Example 1: Even though you did not win the race, take heart from the fact that you did your best. (McGraw-Hill Dict)

Example 2: We told her to take heart and try again next time. I hope she will take heart from what we told her today.

Example 3: The entire world should take heart that progress is being made in the effort to eliminate this disease.(Cambridge Dictinary of American Idioms)

Example 4: House owners can take heart from the news that property prices are starting to rise again.(CID)

[lose heart]