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