Peer demanding attention last of all (4)
I believe the answer is:
earl
'peer' is the definition.
(earl is a kind of peer)
'attention last of all' is the wordplay.
'attention' becomes 'ear' (having someone's ear is having their attention).
'last of' suggests the final letters.
The final letter of 'all' is 'l'.
'ear'+'l'='EARL'
'demanding' acts as a link.
(Other definitions for earl that I've seen before include "Lear (anag)" , "British nobleman" , "Countess his wife" , "A real titled lord" , "Countesss husband" .)