Foolish person’s face might have this urge (3,2)
I believe the answer is:
egg on
This clue is a double definition.
'foolish person's face might have this' is the first definition.
(as in having egg on your face)
'urge' is the second definition.
(to egg someone on is to urge them to do something)
(Other definitions for egg on that I've seen before include "Push" , "Urge, impel" , "Urge (someone) to take risks" , "this face is obvious embarrassment" , "Prod" .)