Take on publicity work, over time (5)
I believe the answer is:
adopt
'take on' is the definition.
(synonyms)
'publicity work over time' is the wordplay.
'publicity' becomes 'ad' (short for advert).
'work' becomes 'op' (abbreviation for opus).
'over' says to put letters next to each other (in a down clue, some letters go over others).
'time' becomes 't' (abbreviation).
'ad'+'op'+'t'='ADOPT'
(Other definitions for adopt that I've seen before include "Embrace" , "make one's own" , "Take responsibility for" , "choose as candidate" , "Take into one's family" .)