At work, prime cut of animals saved in this (3)
I believe the answer is:
ark
'animals saved in this' is the definition.
(Noah's ark)
'at work prime cut' is the wordplay.
'prime' becomes 'two' (prime number).
'cut' indicates named letters should be taken away.
'at'+'work'='atwork'
'atwork' with 'two' taken out is 'ARK'.
'of' is the link.
(Other definitions for ark that I've seen before include "Boat built to withstand floods" , "See 18 Down" , "Coffer" , "Ancient shelter" , "protection for couples that rose in bad weather" .)