Publicly demand that they name quartet, by the sound of things (7)

'they name quartet by the sound of things' is the definition.
I know nothing about this answer so I can't judge whether this works.

'publicly demand' is the wordplay.
I cannot quite see how this works, but
'demand' could be 'call' (call is a kind of demand) and 'call' is present in the answer.
The remaining letters 'for' 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).

'that' acts as a link.

Can you help me to learn more?