For example, cat catching small rat? (4)
I believe the answer is:
pest
'rat?' is the definition.
The definition and answer can be both people as well as being singular nouns.
Maybe there's an association between them I don't understand?
'for example cat catching small' is the wordplay.
'for example cat' becomes 'pet' (cats are often kept as pets).
'catching' means one lot of letters goes inside another.
'small' becomes 's' (abbreviation - e.g. clothes size).
'pet' enclosing 's' is 'PEST'.
Can you help me to learn more?
(Other definitions for pest that I've seen before include "Disease with a high death rate" , "Annoying nuisance" , "Aphis" , "Destructive creature" , "Infernal nuisance" .)