The State agent, with the approval of the Governor, is hereby authorized to enter on behalf of the State into an agreement with the Secretary of the Department of Health, Education and Welfare of the United States, consistent with the terms and provisions of this chapter, for the purpose of extending the benefits of the Federal old age and survivors insurance system to employees of the State or any political subdivision thereof with respect to services specified in such agreement which constitute "employment" as defined in § 9-3-20.