Excellent piano found by Conservative greeting lord's relative (5,10)

'relative' is the definition.
(I know that great grandchild is a type of third-degree relative)

'excellent piano found by conservative greeting lord's' is the wordplay.
I cannot really understand how this works, but
'piano' could be 'grand' (grand piano is a kind of piano) and 'grand' is present in the answer.
'by' could be 'at' and 'at' is located in the answer.
'conservative' could be 'c' (UK political abbreviation) and 'c' is found within the answer.
'greeting' could be 'hi' (hi is a kind of greeting) and 'hi' is found in the answer.
'lord' could be 'ld' (abbreviation for the aristocratic title) and 'ld' is located in the answer.
The remaining letters 'gre' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?