Girl having a rave-up (4)
I believe the answer is:
vera
'girl' is the definition.
'a rave-up' is the wordplay.
'up' indicates an anagram (letters get chucked up).
'rave' with letters rearranged gives 'VERA'.
'having' acts as a link.
(Other definitions for vera that I've seen before include "__ Lynn, the forces' sweetheart" , "Duckworth, Lynn" , "and 15: Singing Dame" , "Woman's name" , "Dame -- Lynn, singer" .)