A couple of hours pet-sitting? (8)
I believe the answer is:
dogwatch
I believe this clue is a double definition.
'a couple of hours' is the first definition.
(two-hour watch on a ship)
'pet-sitting?' is the second definition.
(watching a dog)
(Other definitions for dogwatch that I've seen before include "4-6pm or 6-8pm shift on a ship" , "Short afternoon shift on ship" , "Two-hour period of duty on board ship" , "short spell on board" , "Duty period for ship's complement, kind of canine alert" .)