Dirk upset about a point becomes annoyed (5)
I believe the answer is:
irked
'annoyed' is the definition.
(I've seen this before)
'dirk upset about a point' is the wordplay.
'upset' indicates an anagram.
'about' indicates putting letters inside.
'a point' becomes 'e' (compass point).
'dirk' anagrammed gives 'irkd'.
'irkd' placed around 'e' is 'IRKED'.
'becomes' acts as a link.
(Other definitions for irked that I've seen before include "Irritated, vexed" , "Bugged" , "disgusted" , "Galled" , "Distressed" .)