Publicity, we hear, for a tool (4)
I believe the answer is:
adze
'for a tool' is the definition.
(adze is a kind of tool)
'publicity we hear' is the wordplay.
'publicity' becomes 'ads' (advert).
'we hear' shows a homophone (sound like).
'ads' is a homophone of 'ADZE'.
(Other definitions for adze that I've seen before include "Tool for shaping large pieces of wood" , "Daze with a kind of axe" , "Tool with arched blade set at right angles" , "cutter" , "Wood cutting tool" .)