Give up when drugs, finally, lose their effect (5,3)
I believe the answer is:
swear off
'give up' is the definition.
(thesaurus)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for swear off that I've seen before include "Promise to give (something) up" , "Promise to abstain from - take oath (5, 3)" , "Vow to give up" .)