According to her responses to the New York Times, Gillibrand supports single payer. Private insurance companies could still have a role in providing insurance for elective medical services.
Gillibrand is pro-choice.
She is a co-sponsor of the Green New Deal resolution that Alexandria Ocasio-Cortez (AOC) and Ed Markey introduced in their respective chambers.
According to her website she supports campaign finance reform but does not state if she would break up monopolies.