Communications Security Act This bill provides statutory authority and sets forth membership requirements for a council that provides advice and recommendations to the Federal Communications Commission (FCC) regarding ways to increase the security, reliability, and interoperability of communications networks. The bill specifies that the council must include representatives of companies in the communications industry; public interest organizations or academic institutions; and federal, state, tribal, and local governments (with at least one member representing each level of government). The FCC may designate an existing advisory committee to serve as the council, provided that the committee's membership is modified (if necessary) to comply with the requirements specified in the bill.