Coward's work is to support fighting man (7,5)
I believe the answer is:
private lives
'coward's work' is the definition.
I don't know anything about this answer so I cannot tell whether this works.
'is to support fighting man' is the wordplay.
'is' becomes 'lives' ('he is' means 'he lives').
'to support' says to put letters next to each other (in a down clue, some letters hold up others).
'fighting man' becomes 'private' (private is a kind of man. I am not sure about the 'fighting' bit.).
'lives' after 'private' is 'PRIVATE LIVES'.
Can you help me to learn more?
(Other definitions for private lives that I've seen before include "stage entertainment" , "Play by Noel Coward" , "Noel Coward comedy" .)