Home Office branch last to refurbish fully (2,5)
I believe the answer is:
in depth
'fully' is the definition.
(both can mean in proper detail)
'home office branch last to refurbish' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'office branch' becomes 'dept' (department, part of an office or workplace).
'last to' indicates one should take the final letters.
The final letter of 'refurbish' is 'h'.
'in'+'dept'+'h'='IN-DEPTH'
(Other definitions for in depth that I've seen before include "Penetrating" , "Not 16 [SHALLOW], anyway" , "Detailed sort of investigation" , "full" , "comprehensive" .)