If your offer letter or appointment letter states that you need to give one month's notice or make a payment in lieu of said notice in case of your resignation from company service, the same should still be applicable today. Generally, an employer can modify any existing standing orders/service rules, and as such, they can either enhance or reduce the notice period in case of termination of the services of their employees. However, to do so, they must follow the prescribed procedure as laid down under the standing orders/service rules of the company and notify the same, obtaining the consent of the union or employees if there is no union before implementing such a new term as proposed.
Without notifying the change of service conditions and obtaining the consent of the employee who will be affected by such a change in their existing service conditions, i.e., change of the notice period, etc., which will cause detriment to the interest of an employee, is null and void, and it could not be enforceable under the law.
Hence, explain your case in detail to the HR department of your present employer and tell them to relieve you after completing one month's notice as per your appointment letter if you have already given one month's notice. If they refuse to relieve you after one month, then inform your new employer of the situation. If they agree to take you without having a relieving or service certificate from your existing company, you can join the service of the new company after the lapse of the 30-day notice in your present company.
Regards