Angry corsair loses head (5)
I believe the answer is:
irate
'angry' is the definition.
(irate can mean angry or annoyed)
'corsair loses head' is the wordplay.
'corsair' becomes 'pirate' (I've seen this before).
'loses head' means to remove the first letter.
'pirate' with its initial letter removed is 'IRATE'.
(Other definitions for irate that I've seen before include "Angry - furious" , "Annoyed, irritated" , "Extremely cross" , "Spitting feathers" , "I tear away, being annoyed" .)