A comedy show about to drop pet cat (4)
I believe the answer is:
puma
'cat' is the definition.
(puma is a kind of cat)
'a comedy show about to drop pet' is the wordplay.
'comedy show' becomes 'mu' (I am not sure about this - if you are sure you should believe this answer much more).
'about' shows that the letters should be reversed in order.
'to' says to put letters next to each other (I've seen this in other clues).
'drop' suggests taking the first letters (I've seen 'drop of' mean this).
The initial letter of 'pet' is 'p'.
'a'+'mu'='amu'
'amu' in reverse letter order is 'uma'.
'uma' put after 'p' is 'PUMA'.
(Other definitions for puma that I've seen before include "Mountain lion" , "American wild cat" , "back from Argentina" , "Large American feline resembling a lion" , "South American carnivore" .)