Apartment found in outskirts of Odense in the past few days (2,4)
I believe the answer is:
of late
'in the past few days' is the definition.
(I've seen this before)
'apartment found in outskirts of odense' is the wordplay.
'apartment' becomes 'flat' (synonyms).
'found in' means one lot of letters goes inside another.
'outskirts of' means to remove the middle letters.
'odense' with its middle taken out is 'oe'.
'flat' going within 'oe' is 'OF LATE'.
(Other definitions for of late that I've seen before include "In the recent past" , "Not long ago, in recent times" , "Recently, not long agor" , "recently, not long ago" , "In the past few days" .)