Bird that greatly enjoys fruit, so it's said (4,6)

'greatly enjoys fruit so it's said' is the definition.
I know nothing about this answer so I can't tell whether this works.

'bird' is the wordplay.
I cannot really understand how this works, but
'bird' could be 'plover' (plover is a kind of bird) and 'plover' is located in the answer.
The remaining letters 'grey' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'that' is the link.

Can you help me to learn more?