Giving a lime squash to a girl (6)
I believe the answer is:
amelia
'girl' is the definition.
'giving a lime squash to a' is the wordplay.
'giving' says to put letters next to each other.
'squash' indicates an anagram (I've seen this in other clues).
'to' is a charade indicator (letters next to each other).
'lime' anagrammed gives 'meli'.
'a'+'meli' is 'ameli'.
'ameli'+'a'='AMELIA'
(Other definitions for amelia that I've seen before include "-- Earhart, aviator" , "famous pilot" , "Legless condition" , "Fielding novel" , "Bloomer maybe" .)