Publicity notice detective sergeant puts on (4)
I believe the answer is:
adds
'puts on' is the definition.
(I've seen this before)
'publicity notice detective sergeant' is the wordplay.
'publicity notice' becomes 'ad' (advertisement).
'detective sergeant' becomes 'ds' (abbreviation for detective sergeant).
'ad'+'ds'='ADDS'
(Other definitions for adds that I've seen before include "Sums, totals" , "Goes on to say" , "Joins to something else" , "Finds the sum (4)," , "Calculates the sum" .)