Run away in dunce’s cap, embarrassed (6)
I believe the answer is:
escape
'run away' is the definition.
(to run away is to escape from somewhere)
'in dunce's cap embarrassed' is the wordplay.
'in' indicates a hidden word.
'ESCAPE' can be found hidden inside 'dunces cap embarrassed'.
(Other definitions for escape that I've seen before include "Key < flight" , "Outlet" , "has to fly" , "See cap (anag.)" , "find way out" .)