Departs having taken last of cats' lives (6)
I believe the answer is:
exists
'lives' is the definition.
('exist' can be a synonym of 'live')
'departs having taken last of cats'' is the wordplay.
'departs' becomes 'exits' (I've seen this before**).
'having taken' means one lot of letters goes inside another.
'last of' suggests the final letters.
The last letter of 'cats' is 's'.
'exits' going around 's' is 'EXISTS'.
(Other definitions for exists that I've seen before include "Lives" , "Has objective reality" , "Subsists" , "Has being, is actual" , "Is present in the real world" .)