Dismissal is indicated by this angry-looking oddball (3,4)
I believe the answer is:
red card
'dismissal is indicated by this' is the definition.
(football referees dismiss players with red cards)
'angry-looking oddball' is the wordplay.
'angry-looking' becomes 'red'.
'oddball' becomes 'card' (both can mean an eccentric person).
'red'+'card'='RED CARD'
(Other definitions for red card that I've seen before include "Result of two bookable offences in one game" , "Sending off" , "It signals a serious rule infringement" , "It's shown for a serious infringement of the rules" , "Queen of Hearts, for example" .)