Bighead upset the girl (4)
I believe the answer is:
beth
'girl' is the definition.
(girl's name)
'bighead upset the' is the wordplay.
'bighead' becomes 'b' (head letter of 'big').
'upset' indicates an anagram.
'the' with letters rearranged gives 'eth'.
'b'+'eth'='BETH'
(Other definitions for beth that I've seen before include "character in Israel" , "Hebrew letter; girl's name" , "letter to the Hebrews" , "Little Women sister" , "Concluding stanza" .)