Set out after pet in hiding (5)
I believe the answer is:
doggo
'in hiding' is the definition.
(synonyms)
'set out after pet' is the wordplay.
'set out' becomes 'go' (I can't justify this - if you can you should believe this answer much more).
'after' is a charade indicator (letters next to each other).
'pet' becomes 'dog'.
'go' after 'dog' is 'DOGGO'.
Can you help me to learn more?
(Other definitions for doggo that I've seen before include "hidden away" , "(Lie) in concealment" , "keeping mum out of the picture?" , "(Lie) silent and in hiding" , "in secret" .)