It's a problem to raise hat to a girl (7)
I believe the answer is:
dilemma
'it's a problem' is the definition.
(thesaurus)
'raise hat to a girl' is the wordplay.
'raise' shows that the letters should be reversed in order.
'hat' becomes 'lid' ('lid' can be a synonym of 'hat').
'to a girl' becomes 'emma' (**).
'lid' written backwards gives 'dil'.
'dil'+'emma'='DILEMMA'
'to' acts as a link.
(Other definitions for dilemma that I've seen before include "difficult question" , "Predicament" , "a problem for Shaw's doctor" , "Problem (with horns?)" , "Perplexing situation or difficult choice" .)