Annuity Safety and Security Under Reasonable Enforcement Act of 2013 or the ASSURE Act of 2013 - Amends the Truth in Lending Act to direct the Bureau of Consumer Financial Protection (CFPB) to issue regulations requiring any payment to a recipient of a federal or military pension (a benefit recipient) that diminishes the benefit recipient's ability to control payments from such pension to be treated as an extension of credit.

Requires financial institutions to include the terms of such credit in consumer information disclosures.

Prohibits the annual percentage rate of interest on such arrangements from exceeding the federal funds rate plus 6% or an equivalent aggregate amount of cash and property.

Specifies conditions under which payment of consideration in exchange for the retired pay of enlisted military members is prohibited from assignment under veterans' benefits laws.

Prohibits individuals from making allotments or assignments from annuities under the Civil Service Retirement System (CSRS) or the Federal Employees' Retirement System (FERS), including any agreement under which another person acquires for consideration the right to receive payment from such annuities as well as any arrangement for collateral for security for such an agreement. Exempts union dues or payments to employee organizations from such prohibitions.

Authorizes benefit recipients, individuals entitled to military retired pay, and annuity recipients to bring a private legal action in federal or state court against an assignee engaging in prohibited assignments.

Amends the Consumer Financial Protection Act of 2010 to direct the CFPB to issue regulations requiring persons offering federal or military pension-related products to provide additional disclosures when advertising or selling such products to allow consumers to understand how their pension relates to the product.