Degas perhaps broken by conflict with key enigmatic man (6,5)
I believe the answer is:
edward elgar
'enigmatic man' is the definition.
I don't know anything about this answer so I can't judge whether this works.
'degas perhaps broken by conflict with key' is the wordplay.
'degas perhaps' becomes 'edgar' (I've seen this in another clue. I am not sure about the 'perhaps' bit.).
'broken by' is an insertion indicator (inserted letters break into the word).
'conflict' becomes 'war' (war is a kind of conflict).
'with' means one lot of letters go next to another.
'key' becomes 'del' (Delete on a keyboard).
'war'+'del'='wardel'
'edgar' enclosing 'wardel' is 'EDWARD ELGAR'.
Can you help me to learn more?
(Another definition for edward elgar that I've seen is " British composer of "Enigma Variations"".)