Gets fed up without right links (4)
I believe the answer is:
ties
'links' is the definition.
(tie can mean a connection or link)
'gets fed up without right' is the wordplay.
'gets fed up' becomes 'tires' (becomes fed up or tired).
'without' indicates named letters should be taken away.
'right' becomes 'r' (common abbreviation).
'tires' with 'r' taken out is 'TIES'.
(Other definitions for ties that I've seen before include "Items of neckwear" , "allegiances" , "Connects" , "Binds with male neckwear" , "obligations" .)