In your offer letter or appointment letter, there will be a clause of notice period and the time duration to serve the notice period. Unless you don’t serve the full notice period, you can’t get your relieving letter.
There will a subsection of compensation not for serving notice period under the clause notice period mentioned in your appointment letter or offer letter. If you agree to compensate for not serving the notice period, nobody can stop you from receiving your relieving letter legally.
So, check your offer letter or appointment letter and find out the clause which mentions the compensation from both HR and your side, not for serving the notice period.
New HR wants you to join on immediate basis. You need to check if in the company, there is any option available for buyout notice with the last or new HR. Not serving notice period is compensated from both HR and employee. If it is not given there, you should address it to your HR. They will not relieve you before the notice period and ask you for extra time.
So, check your resignation letter, if there is clearly written your last date working in the company or early reliving date. If it is not mentioned in the resignation letter, you can prepare other resignation letter which has quoted the early resignation date, email date and your last day in office.
Prepare notes which include emails, resources, and docs etc. and you can hand them over to the responsible person and have a signed copy safely with you. This responsible person can be anyone whether he is HR or the manager.
If you have served your notice period, suddenly a new HR has joined and you are not relieved from the current HR still, you can go to the new HR with this issue for it you have to send new HR acceptance copy of resignation.
If you have served your notice period, but you have not get the relieving letter from present HR besides of making requests too many times, the last resort you have is to sue the company. But make sure you have proper documents with you such as the proof that you have served the notice period, appointment letter or offer letter.
Often it happens that on your last working day, HR says that organisation will mail the relieving-cum-experience letter on your personal email-id, but they do not do it for long time and it makes you suffer in the new job for incomplete documentation. In that case, keep pinging previous organisation for the same on mail and phone and if they do not give you the relieving letter, try with labour court and get the matter resolved with their help. You can also visit Ministry of Corporate Affairs website to make a legal complaint against the company. Keep in mind that do not make a negative comments about the organisation on any social media or review website, otherwise it may hamper your relation with the organisation and may increase your wait to collect the letter.
There may be various rules as per companies but no company can deny you from giving relieving letter otherwise law is to rescue you.