Lord Peter has lost heart! (4)
I believe the answer is:
peer
'lord' is the definition.
(I know that peer is a type of lord)
'peter has lost heart' is the wordplay.
'peter has' becomes 'pee' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'lost' becomes 'perdu' (I've seen this before).
'heart' means to look at the middle letters.
The centre of 'perdu' is 'r'.
'pee'+'r'='PEER'
Can you help me to learn more?
(Other definitions for peer that I've seen before include "Social equal" , "Look with concentration; noble" , "Look hard through narrowed eyes" , "Look searchingly at lord?" , "Coequal" .)