Short of Liberal dons? That's annoying (8)
I believe the answer is:
needling
'annoying' is the definition.
(I've seen this before)
'short of liberal dons?' is the wordplay.
'short of' becomes 'needing'.
'liberal' becomes 'l' (abbreviation).
'dons?' means one lot of letters goes inside another.
'needing' going around 'l' is 'NEEDLING'.
'that's' is the link.
(Other definitions for needling that I've seen before include "Doing embroidery" , "Provoking or annoying by continual criticism" , "Aggravating" , "Goading or provoking" , "irksome" .)