In the system there are 3 kinds of clearing members:-
Clearing member cum Trading member:- Who settles his own (pro/clients) trades & others if any.
Self clearing members:- These guy’s settles/ clear’s there own trades.(pro/clients)
Professional Clearing Members:- These members only settles the trades/transactions of the Trading members , whose obligation’s they have accepted to clear or settle.
I think Zerodha’s clearing member is IL&FS.
Clearing members are basically guarantees the settlement of the trades done in the respective exchanges.
Coming to your question , it depends on the category where he belongs to. As explained the first two members can trade in market provided maintain a unique/separate team.