Attention given to Liberal peer (4)
I believe the answer is:
earl
'peer' is the definition.
(earl is a kind of peer)
'attention given to liberal' is the wordplay.
'attention' becomes 'ear' (ear is a kind of attention).
'given to' is a charade indicator (letters next to each other).
'liberal' becomes 'l' (abbreviation).
'ear'+'l'='EARL'
(Other definitions for earl that I've seen before include "A real titled lord" , "Aristocrat ranking between marquis and viscount" , "Count" , "Titled man" , "Husband of a countess" .)