Household pet needs a couple of whips (5-3)
I believe the answer is:
kitty-cat
'household pet' is the definition.
The definition and answer can be both animals as well as being singular nouns.
Perhaps they are linked in a way I don't understand?
'a couple of whips' is the wordplay.
'a couple of whips' can mean two substitutions for 'whip'.
'whip' becomes 'kitty' (I am not sure about this - if you are sure you should believe this answer much more).
'whip' becomes 'cat' (cat o' nine tails, cat for short is a type of whip).
'kitty'+'cat'='KITTY-CAT'
'needs' is the link.
Can you help me to learn more?
(Another definition for kitty-cat that I've seen is " Child's feline pet".)