Complaint about institution's head girl (5)
I believe the answer is:
naomi
'girl' is the definition.
(girl's name)
'complaint about institution's head' is the wordplay.
'complaint' becomes 'moan' (a moan is a complaint or objection).
'about' is a reversal indicator.
'head' indicates taking the first letters.
The first letter of 'institutions' is 'i'.
'moan' written backwards gives 'naom'.
'naom'+'i'='NAOMI'
(Other definitions for naomi that I've seen before include "Ruth's mother-in-law (Old Testament)" , "Ruth's mother-in-law (Bible)" , "mother- in-law" , "Girl's name -- I moan (anag)" , "Biblical mother-in-law of Ruth" .)