Cover up girl's problem that seems incapable of a solution (7)
I believe the answer is:
dilemma
'problem that seems incapable of a solution' is the definition.
(a dilemma is a problem)
'cover up girl's' is the wordplay.
I cannot really understand how this works, but
'cover' could be 'lemma' (lemma is a kind of cover) and 'lemma' is present in the answer.
'girl' could be 'di' and 'di' is found in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for dilemma that I've seen before include "a problem for Shaw's doctor" , "Situation requiring a choice between (equally unpleasant) options" , "Difficult choice; quandary" , "tricky position" , "Predicament" .)