Stimulate progress with promotion (4)
I believe the answer is:
goad
'stimulate' is the definition.
(thesaurus)
'progress with promotion' is the wordplay.
'progress' becomes 'go' (I've seen this in other clues).
'with' means one lot of letters go next to another.
'promotion' becomes 'ad' (ad is a kind of promotion).
'go'+'ad'='GOAD'
(Other definitions for goad that I've seen before include "Incentive" , "Prod with a pointed stick" , "Provoke to action" , "Prompt" , "Cattle-driving spike" .)