Can we directly talk to clients, are they willing to hire me in their company?

U can call and ask them if they have any opportunity for ur role in their company .. even if they have, TCS has to give noc certificate..

There should be a cooling period at least 6 months

You can talk, but most tcs contract with customer stipulate that do not hire tcs employee within 6 months when a person last worked with them... So in most cases client won't agree unless you are really needed and their team is ready to negotiate with tcs.