Must have fish? That's annoying (8)
I believe the answer is:
needling
'annoying' is the definition.
(I've seen this before)
'must have fish?' is the wordplay.
'must' becomes 'need' ('need' can be a synonym of 'must').
'have' says to put letters next to each other.
'fish?' becomes 'ling' (ling is a kind of fish).
'need'+'ling'='NEEDLING'
'that's' acts as a link.
(Other definitions for needling that I've seen before include "irksome" , "Aggravating" , "Provoking or annoying by continual criticism" , "Goading or provoking" , "Doing embroidery" .)