Supported child quietly admitted to this and flushed (9)
I believe the answer is:
sponsored
'supported' is the definition.
(sponsoring is a kind of supporting)
'child quietly admitted to this and flushed' is the wordplay.
I cannot quite see how this works, but
'quietly' could be 'p' (p for piano and quiet) and 'p' is present in the answer.
'child' could be 'son' (male child) and 'son' is located in the remaining letters.
'flushed' could be 'red' (red-faced) and 'red' is present in the answer.
The remaining letters 'so' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for sponsored that I've seen before include "With backing" , "(Of event) supported financially" .)