Meaning of “give up (sth)” - Learner’s Dictionary

give up (sth)

phrasal verb with give uk us /ɡɪv/ verb (past tense gave, past participle given)

B1 If you give up a habit such as smoking, or give up something unhealthy such as alcohol, you stop doing it or having it:

I gave up smoking two years ago.

B1 to stop doing something before you have completed it, usually because it is too difficult:

[ + doing sth ] I've given up trying to help her.

(Definition of “give up (sth) phrasal verb, verb” from the Cambridge Learner’s Dictionary © Cambridge University Press)