Completely gave up nicotine at the end (5)
I believe the answer is:
quite
'completely' is the definition.
(synonyms in phrases like 'are you quite done?')
'gave up nicotine at the end' is the wordplay.
'gave up' becomes 'quit' (quit can mean to give up).
'at the end' indicates one should take the final letters.
The last letter of 'nicotine' is 'e'.
'quit'+'e'='QUITE'
(Other definitions for quite that I've seen before include "Rather" , "To a degree" , "Somewhat - I agree" , "Completely or entirely - be quiet" , "Fairly; indeed" .)