Behind closed doors, centre is being refurbished (2,6)
I believe the answer is:
in secret
'behind closed doors' is the definition.
(I've seen this in another clue)
'centre is being refurbished' is the wordplay.
'being refurbished' indicates anagramming the letters.
'centre'+'is'='centreis'
'centreis' is an anagram of 'IN SECRET'.
(Other definitions for in secret that I've seen before include "Without others knowing" , "behind closed doors" , "Covertly" , "privately" , "Confidentially" .)