My employer is refusing to release me after submitting resignation

Hello, I am employed through a workforce org: called TeamLease digital who have contracted with Novartis, who is the client I am serving. I have resigned from my duties today - 5/18/2021. My notice period is set to 30 days after 6 months of probation. However, my employer is stating that 30 days notice is too short and has not confirmed on a release date. What's worse is that my HR from TeamLease, through whom I'm contracted, is hand-in-glove with my manager and is stating that the 30 days notice is subject to my manager's approval. Under the separation clause in my offer letter, the below is stated: 11. Separation: In the event you wish to leave the services of the Company, you will be required to give a clear written notice of 15 days to the Company in probation period for fisrt 6months after completion of your probation period its 30 days notice. You will be relieved from the services of the Company subject to your. a. Handing over the project and knowledge transfer to the client’s assigned representative/s in respect of the assignments handled by you. b. Obtaining a “No Objection Letter” from the client as a confirmation of your having complied with (a) above. What can I do?