Arrogant type stumped in posh role (7)
I believe the answer is:
'arrogant type' is the definition.
(I've seen this before)
'stumped in posh role' is the wordplay.
'stumped' becomes 'st' (cricket abbreviation).
'in' means one lot of letters goes inside another.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-U).
'role' becomes 'part' (eg a part or role in a film).
'st' placed into 'upart' is 'UPSTART'.
(Other definitions for upstart that I've seen before include "Unexpectedly fresh" , "Person who has suddenly risen in wealth or importance" , "New and arrogant arrival at high position" , "Person newly risen from the ranks and arrogant" , "Person suddenly risen in world, and arrogant" .)