Crossword Genius

The sound of fun has Liberal going for Democrat progeny (8)

Ross

I believe the answer is:

daughter

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

'progeny' is the definition.
(I know that progeny can be written as daughter)

'the sound of fun has liberal going for democrat' is the wordplay.
I cannot quite see how this works, but
an anagram of 'the' is 'hte' which is present in the answer.
'democrat' could be 'd' and 'd' is found within the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for daughter that I've seen before include "Relation" , "'''Don't put your ... on the stage, Mrs Worthington'' (Noel Coward) (8)'" , "Female child" , "Close relative" , "Girl" .)

I've seen this clue in The Telegraph.
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