Annoyed by a keen beginner in dire trouble (5)
I believe the answer is:
irked
'annoyed' is the definition.
(I've seen this in another clue)
'a keen beginner in dire trouble' is the wordplay.
'beginner' suggests taking the first letters.
'in' is an insertion indicator.
'trouble' indicates anagramming the letters.
The first letter of 'keen' is 'k'.
'dire' anagrammed gives 'ired'.
'k' put inside 'ired' is 'IRKED'.
'by' acts as a link.
(Other definitions for irked that I've seen before include "Wound" , "Galled" , "Irritated, vexed" , "Distressed" , "Exasperated" .)