Exhausted MEP's upset relationship with leader of Denmark (7)
I believe the answer is:
emptied
'exhausted' is the definition.
(I've seen this before)
'mep's upset relationship with leader of denmark' is the wordplay.
'upset' indicates an anagram.
'relationship' becomes 'tie' (tie is a kind of relationship).
'with' says to put letters next to each other.
'leader of' indicates taking the first letters.
The initial letter of 'denmark' is 'd'.
'mep' with letters rearranged gives 'emp'.
'emp'+'tie'+'d'='EMPTIED'
(Other definitions for emptied that I've seen before include "Made vacant" , "Made void" , "Drained" , "having nothing more to offer" , "was draining" .)