If a local social security payment stops and a new account is opened in another city, does the social security period accumulate?

Yes, the payment period is counted together. According to Article 3 of the Notice on Forwarding the Interim Measures for the Transfer and Continuation of the Basic Old-age Insurance for Urban Enterprise Employees in Ministry of Human Resources and Social Security and the Ministry of Finance, if the insured person is employed across provinces, the social insurance agency where the original insured person is located (hereinafter referred to as the social insurance agency) shall issue the certificate of payment for the insurance, and the basic old-age insurance relationship shall be transferred to the new insured place. If the insured reaches the conditions for receiving the basic old-age insurance benefits, the payment period of insurance premiums will be calculated together, and the amount of personal account storage (including principal and interest, the same below) will be calculated cumulatively; Before reaching the age of receiving treatment, the basic old-age insurance relationship shall not be terminated, and the procedures for surrender shall be handled; Let the original company help you with the transfer procedures and give you a proof of payment of endowment insurance and medical insurance. You just need to give this certificate to your new company to help you, and the internal procedures of social security will be solved internally.