Angry corsair loses his head (5)
I believe the answer is:
irate
'angry' is the definition.
(irate can mean angry or annoyed)
'corsair loses his head' is the wordplay.
'corsair' becomes 'pirate' (I've seen this in another clue).
'loses his head' means to remove the first letter.
'pirate' with its initial letter taken away is 'IRATE'.
(Other definitions for irate that I've seen before include "Annoyed, nettled" , "Mad" , "Cross, irritated" , "Hacked off" , "Wild" .)