Nuisance not having answer: girl in quandary (8)
I believe the answer is:
trilemma
'quandary' is the definition.
(choice between three options)
'nuisance not having answer girl' is the wordplay.
'nuisance' becomes 'trial' (both can mean something annoying).
'not having' suggests deleting specific letters.
'answer' becomes 'a' (abbreviation eg in Q and A).
'girl' becomes 'emma' (girl's name).
'trial' with 'a' taken away is 'tril'.
'tril'+'emma'='TRILEMMA'
'in' acts as a link.
(Other definitions for trilemma that I've seen before include "one posing some nasty choices" , "Quandary" .)