A problem a woman with loud independent sect may finish (10)
I believe the answer is:
difficulty
'a problem' is the definition.
(thesaurus)
'with loud independent sect may finish' is the wordplay.
'with' indicates putting letters inside.
'loud' becomes 'ff' (short for fortissimo - 'very loud' in music).
'independent' becomes 'i'.
'sect' becomes 'cult' (I've seen this before).
'may finish' becomes 'diy' (I can't justify this - if you can you should give a lot more credence to this answer).
'ff'+'i'+'cult'='fficult'
'fficult' placed inside 'diy' is 'DIFFICULTY'.
'a woman' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?