Exist to chase round girl? (5)
I believe the answer is:
olive
'girl?' is the definition.
'exist to chase round' is the wordplay.
'exist' becomes 'live' ('live' can be a synonym of 'exist').
'to chase' is a charade indicator (letters next to each other).
'round' becomes 'o' (round can mean a round object).
'live' after 'o' is 'OLIVE'.
(Other definitions for olive that I've seen before include "A Med. fruit-tree" , "Bitter fruit" , "Mediterranean tree-fruit - nice in martini" , "Mediterranean fruit or greenish colour" , "Its branch is a peace emblem" .)