Privacy Notice Modernization Act of 2013 - Amends the Gramm-Leach-Bliley Act to exempt from its annual written privacy policy notice requirement any financial institution which: (1) provides nonpublic personal information only in accordance with specified requirements, (2) has not changed its policies and practices with respect to disclosing nonpublic personal information from those disclosed in the most recent disclosure sent to consumers, and (3) otherwise provides customers access to such most recent disclosure in electronic or other form permitted by specified regulations.