Number one is obsessive about, say ... (6)
I believe the answer is:
animal
'say' is the definition.
Although both the answer and definition are singular nouns, I don't understand how one could define the other.
'number one is obsessive about' is the wordplay.
'number one is' becomes 'I'm' (number one can refer to oneself).
'obsessive' becomes 'anal' (I've seen this before).
'about' means one lot of letters goes inside another.
'im' put into 'anal' is 'ANIMAL'.
(Other definitions for animal that I've seen before include "Beastly" , "Such as 13 ac" , "Any organism capable of voluntary movement" , "See 26" , "Mammal" .)