Like best running about with the dog (6)
I believe the answer is:
basset
'the dog' is the definition.
(basset is a kind of dog)
'like best running about' is the wordplay.
'like' becomes 'as'.
'running' indicates an anagram.
'about' indicates putting letters inside.
'best' is an anagram of 'bset'.
'as' put into 'bset' is 'BASSET'.
'with' acts as a link.
(Other definitions for basset that I've seen before include "Short-legged hound used for hunting (6)Short-legged hound used for hunting" , "Short-legged hound that hunts hares" , "Hound with short legs and long ears" , "Hound (named Fred?)" , "Hare-hunting hound among beasts" .)