It runs round tree, as dog does (4)
I believe the answer is:
bark
This clue is a double definition.
'it runs round tree' is the first definition.
(a tree has bark around it)
'as dog does' is the second definition.
(dogs bark)
(Other definitions for bark that I've seen before include "Sailing-ship" , "Cry of a dog or fox" , "Cri de cur?" , "possibly causing alarm in 23 [CATTERY] ?" , "Protective covering of woody stems" .)