Apartment in Odense gutted recently (2,4)
I believe the answer is:
of late
'recently' is the definition.
('of late' can be a synonym of 'recently')
'apartment in odense gutted' is the wordplay.
'apartment' becomes 'flat' ('flat' can be a synonym of 'apartment').
'in' is an insertion indicator.
'gutted' means to remove the middle letters (to gut something is to remove its insides).
'odense' with its centre taken out is 'oe'.
'flat' placed within 'oe' is 'OF LATE'.
(Other definitions for of late that I've seen before include "recently, not long ago" , "Not long ago, in recent times" , "In the past few days" , "In the recent past" , "Recently, not long agor" .)