Change neat order and take turns (9)
I believe the answer is:
alternate
'take turns' is the definition.
(synonyms)
'change neat order' is the wordplay.
'change' becomes 'alter' (synonyms).
'order' indicates an anagram.
'neat' with letters rearranged gives 'nate'.
'alter'+'nate'='ALTERNATE'
'and' acts as a link.
(Other definitions for alternate that I've seen before include "go back and forth" , "Happening or following in turns, one after the other" , "Every second one of a series" , "Occurring in turn repeatedly" , "Occur in turn repeatedly" .)