As part of Thursday’s agreement, First Allmerica also agreed to make remedial efforts totaling about $40 million, including waiving some back premiums or extending payments for policyholders who didn’t receive notices, New York’s Department of Financial Services said.

“Insurers who outsource their responsibilities to third parties are still responsible to meet all of their obligations under the law,” said New York Financial Services Superintendent Maria T. Vullo in a statement.

According to the consent order, Athene failed to mail notices about premium due dates for a total of $81 million in premiums, among other violations.

“Athene has a strong commitment and track record of providing high quality service to its policyholders and will continue to work with [First Allmerica] as the remediation matters are implemented,” Athene said.

“We are doing everything possible to ensure policy owners’ interests are protected, and throughout this process policyholder benefits remained in force and we have paid claims,” Global Atlantic said in a statement.

Earlier this month, the California Department of Insurance served an order to show cause and accusation against Athene and another unit of Global Atlantic for failing to service more than 50,000 life policies.

Nicole Friedman at nicole.friedman@wsj.com