Short answer to your question is "Yes". But you will get a new agency not the reinstatement of old agency.

As per Guidelines on appointment of Insurance Agents, 2015

Procedure to be followed in respect of resignation/surrender of appointment by an insurance agent:

1) In case an insurance agent appointed by an insurer wishes to surrender his agency with his/her insurer, he/she shall surrender his appointment letter and identity card to the designated official of the insurer with whom he/she is currently holding agency.

2) The Insurer shall issue the cessation certificate as detailed in Form 1-C within a period of 15 days from the date of resignation or surrender of appointment.

3) An agent who has surrendered his appointment may seek fresh appointment with other insurer. In such a case, the agent has to furnish to the new insurer all the details of his/her previous agency and produce Cessation Certificate issued by the previous insurer issued in Form I-C, along with his agency application form.

4) The insurer will consider the agency application as outlined in Clause IV after a period of NINETY DAYS from the date of the issue of the cessation certificate by the previous insurer.