Not quite the place for the dead cat (3)
I believe the answer is:
tom
'cat' is the definition.
(a tom is a male cat)
'not quite the place for the dead' is the wordplay.
'not quite' means to remove the last letter (most but not all of the word).
'the place for the dead' becomes 'tomb' (burial place).
'tomb' with its final letter taken away is 'TOM'.
(Other definitions for tom that I've seen before include "type pursuing queen" , "Waits, perhaps" , "- Lehrer, US humorist" , "Cruise" , "Queen's mate" .)