Publicise search for weapon (3,5)
I believe the answer is:
air rifle
'weapon' is the definition.
(I've seen this before)
'publicise search' is the wordplay.
'publicise' becomes 'air' (synonyms).
'search' becomes 'rifle' (I've seen this before).
'air'+'rifle'='AIR-RIFLE'
'for' acts as a link.
(Other definitions for air rifle that I've seen before include "Pellet gun" , "Rail fire (anag) - weapon" , "One shoots pellets" , "Fire liar (anag)" , "Shooter" .)