Crossword Genius

Old musician has piece to play after lifting of short stick (4,6)

Ross

I believe the answer is:

fats domino

I'm a little stuck... Click here to teach me more about this clue!

'old musician' is the definition.
(I know that Fats Domino is a rhythm and blues musician)

'piece to play after lifting of short stick' is the wordplay.
I cannot really see how this works, but
'piece' could be 'fat' (fat is a kind of piece) and 'fat' is found in the answer.
'play' could be 'no' (no or noh is a type of Japanese theatre) and 'no' is located in the answer.
'of' could be 'o' and 'o' is present in the answer.
This explanation may well be incorrect...

'has' is the link.

Can you help me to learn more?

(Another definition for fats domino that I've seen is " "Ain't That a Shame" singer and pianist".)

I've seen this clue in The Times.
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