A part-time worker captivated by non-drinker’s endeavour (7)
I believe the answer is:
attempt
'endeavour' is the definition.
(synonyms)
'a part-time worker captivated by non-drinker's' is the wordplay.
'part-time worker' becomes 'temp' (a temporary office worker).
'captivated by' is an insertion indicator.
'non-drinker' becomes 'tt' (abbreviation for teetotaller).
'temp' inserted into 'tt' is 'ttempt'.
'a'+'ttempt'='ATTEMPT'
(Other definitions for attempt that I've seen before include "Undertake" , "Essay" , "Have a crack" , "Endeavor, try" , "Try to climb (a peak)" .)