After short time employer gets cat (6)
I believe the answer is:
mouser
'cat' is the definition.
(mouser is a kind of cat)
'after short time employer' is the wordplay.
'after' says to put letters next to each other.
'short time' becomes 'mo' (slang abbreviation for 'moment').
'employer' becomes 'user' (I've seen this before).
'mo'+'user' is 'MOUSER'.
'gets' is the link.
(Other definitions for mouser that I've seen before include "pest controller" , "Useful mog" , "Rodent-catching cat" , "Cat proficient at catching small rodents" , "Cat as hunter of small rodents" .)