noun-modifying (irregular)
Prenominal modifier describing a person, action, or decision that shows courage.
He made a courageous decision.
I was moved by the brave action.
勇気 is the noun 'courage'; 勇気ある is the adnominal form meaning 'courageous' or 'brave'.
Standard spelling using ある in kana.
Rare variant using the kanji 有る; the kana spelling ある is strongly preferred in modern Japanese.
Compound of 勇気 (courage) + ある (to have, exist), literally 'having courage'. The spelling 有る is etymologically related but now rare.