Quandary of Miss Woodhouse perhaps, after returning hat (7)
I believe the answer is:
dilemma
'quandary' is the definition.
(synonyms)
'miss woodhouse perhaps after returning hat' is the wordplay.
'miss woodhouse perhaps' becomes 'Emma' (main character in Jane Austen's novel Emma).
'after' is a charade indicator (letters next to each other).
'returning' says the letters should be written backwards.
'hat' becomes 'lid' (lid can informally mean a hat).
'lid' backwards is 'dil'.
'emma' after 'dil' is 'DILEMMA'.
'of' acts as a link.
(Other definitions for dilemma that I've seen before include "embarrassment" , "Shavian doctor's problem" , "The choice between courses of action, all equally undesirable" , "Difficulty (with two choices?)" , "Awkward situation" .)