Peer pressure ultimately applied against a heartless prince (4)
I believe the answer is:
earl
'peer' is the definition.
(I know that earl is a type of peer)
'pressure ultimately applied against a heartless prince' is the wordplay.
'pressure ultimately' becomes 'ea' (I am not sure about this - if you are sure you should believe this answer much more).
'applied against' says to put letters next to each other (some letters go against others).
'a heartless' means to remove the middle letters.
'prince' becomes 'royal' (prince is a type of royal).
'royal' with its centre taken out is 'rl'.
'ea'+'rl'='EARL'
(Other definitions for earl that I've seen before include "British nobleman" , "Noble title" , "Countess his wife" , "A real titled lord" , "A lord like Lear" .)