Does trainer broadcast a topic in metaphysics? (6,5)
I believe the answer is:
raison detre
'a topic in metaphysics?' is the definition.
(French phrase meaning 'reason for being')
'does trainer broadcast' is the wordplay.
'broadcast' is an anagram indicator (letters scattered or cast around).
'does'+'trainer'='doestrainer'
'doestrainer' is an anagram of 'RAISON DETRE'.
(Other definitions for raison detre that I've seen before include "Purpose of existence" , "existing motive?" , "Justification for existence" , "Reason for living" , "Reason for existence (6,1'4)" .)