Adult joint's style of music (9)
I believe the answer is:
bluegrass
'music' is the definition.
(I've seen this before)
'adult joint's style' is the wordplay.
'adult' becomes 'blue' (I've seen this before).
'joint's style' becomes 'grass' (I can't explain this - if you can you should give a lot more credence to this answer).
'blue'+'grass'='BLUEGRASS'
'of' is the link.
Can you help me to learn more?
(Other definitions for bluegrass that I've seen before include "Style of US country music" , "nickname of US State" , "A type of country music" , "Kind of country music" , "American hillbilly music" .)