To hunger is to “crave ardently,” and those who thirst “painfully feel their want of, and eagerly long for, those things by which the soul is refreshed, supported, strengthened …” according to Thayer’s Greek Lexicon.
This fourth Beatitude tells us what will satisfy that craving … righteousness.
“you are in Christ Jesus, who became to us wisdom from God, righteousness and sanctification and redemption,” 1 Corinthians 1:30
and He will give you the desires of your heart. Psalm 37:4