The cover-up woman is the problem (7)
I believe the answer is:
'the problem' is the definition.
(a dilemma is a problem)
'the cover-up woman' is the wordplay.
I cannot really see how this works, but
'cover' could be 'lemma' (lemma is a kind of cover) and 'lemma' is located in the answer.
'woman' could be 'di' (short for Diana) and 'di' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'is' acts as a link.
Can you help me to learn more?
(Other definitions for dilemma that I've seen before include "embarrassment" , "Situation requiring a choice between (equally unpleasant) options" , "I'm lamed - it's a puzzle" , "Difficulty (with two choices?)" , "Difficult problem" .)