Pole in wrong gear shows annoyance (5)
I believe the answer is:
anger
'annoyance' is the definition.
(I've seen this in other clues)
'pole in wrong gear' is the wordplay.
'pole' becomes 'n' (abbreviation for North, as in North Pole).
'in' means one lot of letters goes inside another.
'wrong' indicates an anagram.
'gear' anagrammed gives 'ager'.
'n' inserted into 'ager' is 'ANGER'.
'shows' is the link.
(Other definitions for anger that I've seen before include "wind up?" , "Hostile feeling" , "Annoyance, displeasure" , "Rage" , "blaze of this?" .)