Cook keeps close to au pair (3)
I believe the answer is:
duo
'pair' is the definition.
('duo' can be a synonym of 'pair')
'cook keeps close to au' is the wordplay.
'cook' becomes 'do' (I've seen this in other clues**).
'keeps' is an insertion indicator.
'close to' says to take the final letters (the close/ending of).
The final letter of 'au' is 'u'.
'do' going around 'u' is 'DUO'.
(Other definitions for duo that I've seen before include "They might play" , "Pair of performers" , "Music for two" , "Performing couple" , "Musical pair" .)