Plebeian at heart desires property (10)
I believe the answer is:
belongings
'property' is the definition.
(I've seen this before)
'plebeian at heart desires' is the wordplay.
'at heart' means to look at the middle letters.
'desires' becomes 'longings' (longing is a kind of desire).
The centre of 'plebeian' is 'be'.
'be'+'longings'='BELONGINGS'
(Other definitions for belongings that I've seen before include "property" , "stuff" , "Personal effects" .)