Mythical creature and dog have neat arrangement (7)
I believe the answer is:
centaur
'mythical creature' is the definition.
(centaur is a kind of mythical creature)
'dog have neat arrangement' is the wordplay.
'dog' becomes 'cur' (cur is a kind of dog).
'have' is an insertion indicator.
'arrangement' indicates an anagram.
'neat' is an anagram of 'enta'.
'cur' going around 'enta' is 'CENTAUR'.
'and' acts as a link.
(Other definitions for centaur that I've seen before include "Greek mythical creature" , "Mythical man-horse" , "Mythical semi-equine beast" , "Fabulous horse-man" , "Half-man and half horse" .)