Near West End, impose limit on drink (8)
I believe the answer is:
nightcap
'drink' is the definition.
(I have seen 'Late drink ' mean 'nightcap' so perhaps 'drink' could also mean 'nightcap')
'near west end impose limit on' is the wordplay.
'near' becomes 'nigh' ('nigh' can be a synonym of 'near').
'end' indicates one should take the final letters.
'impose limit on' becomes 'cap' (I've seen this before).
The final letter of 'west' is 't'.
'nigh'+'t'+'cap'='NIGHTCAP'
(Other definitions for nightcap that I've seen before include "Take before bed or wear in bed" , "Head covering" , "what last drink might be" , "drink having sleepy effect?" , "attire" .)