Annoyed by a shifty pest at the youth centre (5)
I believe the answer is:
upset
'annoyed' is the definition.
(I've seen this before)
'a shifty pest at the youth centre' is the wordplay.
'a shifty' indicates anagramming the letters.
'at' says to put letters next to each other (I've seen this in other clues).
'centre' says to take the centre.
The middle letter of 'youth' is 'u'.
'pest' is an anagram of 'pset'.
'pset' after 'u' is 'UPSET'.
'by' acts as a link.
(Other definitions for upset that I've seen before include "Aggrieved" , "Overturn; distress" , "Surprise result" , "Disturb, physically or emotionally" , "Make unhappy; disrupt" .)