Cover up Miss Woodhouse's awkward situation (7)
I believe the answer is:
dilemma
'awkward situation' is the definition.
(I've seen this before)
'cover up miss woodhouse's' is the wordplay.
'cover' becomes 'lid' (lid is a kind of cover).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'miss woodhouse' becomes 'Emma' (main character in Jane Austen's novel Emma).
'lid' reversed gives 'dil'.
'dil'+'emma'='DILEMMA'
(Other definitions for dilemma that I've seen before include "tricky position" , "Catch-22" , "Difficult decision" , "doubtful state" , "Difficult choice; quandary" .)