Crossword Genius

Publicity, we hear, for a tool (4)

Ross

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' indicates a 'sounds like' (homophone) clue.
'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" .)

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