Composer of old, once with movement about conflict (4,6)
I believe the answer is:
noel coward
'composer' is the definition.
(playwright and songwriter)
'old once with movement about conflict' is the wordplay.
'with movement' indicates anagramming the letters (letters move around).
'about' indicates putting letters inside.
'conflict' becomes 'war' (war is a kind of conflict).
'old'+'once'='oldonce'
'oldonce' with letters rearranged gives 'noelcod'.
'noelcod' placed around 'war' is 'NOEL COWARD'.
'of' acts as a link.
(Other definitions for noel coward that I've seen before include "dramatist" , "Old playwright" , "He wrote" .)