Screen producer’s turkey chasing small donkey (5,4)
I believe the answer is:
smoke bomb
'screen producer's' is the definition.
(something which might produce a smoke screen)
'turkey chasing small donkey' is the wordplay.
'turkey' becomes 'bomb' ('bomb' can be a synonym of 'turkey').
'chasing' means one lot of letters go next to another.
'small' becomes 's' (abbreviation - e.g. clothes size).
'donkey' becomes 'moke' (moke is a kind of donkey).
's'+'moke'='smoke'
'bomb' after 'smoke' is 'SMOKE-BOMB'.
(Other definitions for smoke bomb that I've seen before include "Explosive position marker" , "this may cover aggressive activity" , "Pyrotechnic obscurant" , "Weapon providing concealment" , "One set off to obscure" .)