Company in rush to get cat (7)
I believe the answer is:
scourge
'cat' is the definition.
(I've seen this before)
'company in rush' is the wordplay.
'company' becomes 'co' (abbreviation).
'in' means one lot of letters goes inside another.
'rush' becomes 'surge' ('surge' can be a synonym of 'rush'**).
'co' put inside 'surge' is 'SCOURGE'.
'to get' acts as a link.
(Other definitions for scourge that I've seen before include "Harass" , "One providing lashings" , "Pest" , "Plague; whip" , "Affliction - whip" .)