Hi Sudheendra,
Most of the companies issues the relieving letter on the last working day of the employee provided all the exit formalities were completed. Experience letter will be sent to employees within a week or 10 business days.
Meanwhile, if candidate has to join the new employer, he/she can show the relieving letter and can inform that the experience letter will follow. HRs are aware of this and on this intention the relieving letter being issued.
In your case, as you already have the experience certificate, it would suffice the new employer requirements. And if the new employer ask for relieving letter, you can refer to the old employer for any reference.
The purpose of the relieving letter is to show that, you are relived from the service of the company from X date. And this info is already in experience certificate so no issues.
Regards
Thiyagu