Dawn entertaining male priest in glare of publicity (9)
I believe the answer is:
limelight
'glare of publicity' is the definition.
(I've seen this before)
'dawn entertaining male priest' is the wordplay.
'dawn' becomes 'light' (I've seen this before).
'entertaining' means one lot of letters goes inside another (inviting in, as for dinner).
'male' becomes 'm' (common abbreviation).
'priest' becomes 'eli' (biblical figure).
'm'+'eli'='meli'
'light' enclosing 'meli' is 'LIMELIGHT'.
'in' acts as a link.
(Other definitions for limelight that I've seen before include "Charlie Chaplin film" , "A theatrical glower" , "The glare of publicity" , "having prominence on stage" , "centre of public attention" .)