Pet outside home is performing (5)
I believe the answer is:
doing
'is performing' is the definition.
(I've seen this before)
'pet outside home' is the wordplay.
'pet' becomes 'dog'.
'outside' indicates putting letters inside.
'home' becomes 'in' ('he's home' can mean 'he's in').
'dog' placed around 'in' is 'DOING'.
(Other definitions for doing that I've seen before include "Faring" , "Carrying out action" , "Beating (colloquial); performing" , "Performing a task" , "Execution" .)