Complain of a broken-down pier at Gateshead (5)
I believe the answer is:
gripe
'complain' is the definition.
(I know that gripe is a more specific form of the action complain)
'a broken-down pier at gateshead' is the wordplay.
'a broken down' indicates an anagram.
'at' means one lot of letters go next to another (I've seen this in other clues).
'gateshead' becomes 'g' (head letter of 'gates').
'pier' with letters rearranged gives 'ripe'.
'ripe' put after 'g' is 'GRIPE'.
'of' is the link.
(Other definitions for gripe that I've seen before include "Trivial complaint" , "Complain; colic (water)" , "beef" , "Protest" , "Keep on complaining" .)