Suppress cover in the middle of Greece (5)
I believe the answer is:
elide
'suppress' is the definition.
(I've seen this before)
'cover in the middle of greece' is the wordplay.
'cover' becomes 'lid' (lid is a kind of cover).
'in the' is an insertion indicator.
'middle of' means to look at the middle letters.
The centre of 'greece' is 'ee'.
'lid' placed into 'ee' is 'ELIDE'.
(Other definitions for elide that I've seen before include "Abridge, omit part" , "Suppress - abridge" , "Omit part of word" , "Cut off" , "Drop off" .)