Tramp's dog's maybe running round (4)
I believe the answer is:
step
'tramp's' is the definition.
(to tramp is to step heavily)
'dog's maybe running round' is the wordplay.
'dog's maybe' becomes 'pet's' (dogs are often kept as pets).
'running round' shows that the letters should be reversed in order.
'pets' in reverse letter order is 'STEP'.
(Other definitions for step that I've seen before include "Footfall" , "Bit of mashed potato maybe" , "Second half of quick 20?" , "Pace - part of a procedure" , "Set foot down on pest" .)