That man's failing, mate -- but he's still in office (4)
'he's still in office' is the definition.
(British politician Matt Hancock)
'that man's failing mate' is the wordplay.
'failing' indicates anagramming the letters.
'mate' becomes 'cock' (both are terms of affection).
'that'+'man'='thatman'
'thatman' anagrammed gives 'matthan'.
'matthan'+'cock'='MATT HANCOCK'
'but' is the link.
'he's still in office' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'that man's failing mate' is the wordplay.
'that man' becomes 'm'.
'failing mate' becomes 'att' (I can't justify this - if you can you should give a lot more credence to this answer).
'm'+'att'='MATT'
'but' acts as a link.
Can you help me to learn more?
(Other definitions for matt that I've seen before include "book" , "- Lucas (Little Britain)" , "Without a shine, dull" , "Non-gloss" , "Dull uniform finish" .)