A company that accepts loss exposure from another insurer in a reinsurance contract is called the

A subscriber typically refers to an individual or entity that pays to receive a service or a product, such as a magazine or streaming service. In the context of insurance, the term does not apply to the role of accepting loss exposure from another insurer, making it an incorrect choice.

The primary insurer is the original insurance company that directly covers the insured risks. While it is responsible for underwriting policies and handling claims from policyholders, it is not the entity that accepts risks from another insurer, and therefore, does not fit the definition provided in the question.

A private insurer is a company that provides insurance policies to individuals or businesses but operates independently of government involvement. While they can be either primary insurers or reinsurers, the term does not specifically refer to the entity that accepts loss exposure from another insurer, making it an inaccurate choice for this question.