Grandee’s pet crossing river with heartless Italian poet (10)
I believe the answer is:
aristocrat
'grandee's' is the definition.
(thesaurus)
'pet crossing river with heartless italian poet' is the wordplay.
'pet crossing river' becomes 'crat' (I can't explain this - if you can you should give a lot more credence to this answer).
'with' says to put letters next to each other.
'heartless' means to remove the middle letters.
'italian poet' becomes 'ariosto' (Ludovico Ariosto).
'ariosto' with its middle taken out is 'aristo'.
'crat' put after 'aristo' is 'ARISTOCRAT'.
(Other definitions for aristocrat that I've seen before include "Member of the upper class" , "What's listed in Debrett" , "Noble" , "toff" , "Member of the nobility" .)