Isle that includes central Kent, oddly enough (6)
I believe the answer is:
thanet
'isle' is the definition.
(I've seen this before)
'that includes central kent oddly enough' is the wordplay.
'includes' indicates putting letters inside.
'central' says to take the centre.
'oddly enough' indicates anagramming the letters.
The central letters of 'kent' are 'en'.
'en' with letters rearranged gives 'ne'.
'that' going around 'ne' is 'THANET'.
(Other definitions for thanet that I've seen before include "Isle in Kent" , "Northeast part of Kent" , "District of Kent" , "Area of Kent, an island in name only" , "Area of Kent which was an island until C 16" .)