Throw out that dud vet, I see! (5)
I believe the answer is:
evict
'throw out' is the definition.
(evicting is a kind of throwing out)
'dud vet i see' is the wordplay.
'dud' indicates an anagram.
'see' becomes 'c' (the word for the letter, according to Chambers).
'vet'+'i'+'c'='vetic'
'vetic' is an anagram of 'EVICT'.
'that' is the link.
(Other definitions for evict that I've seen before include "Remove from a residence" , "remove someone" , "Cast out" , "Throw from the premises" , "Remove form house for non-payment" .)