This claim appears to be true. The original post from @environment on instagram claims that Taylor Swift is taking legal action against Jack Sweeney, a university student from Florida, for tracking her plane routes. Upon doing further research, I found more information that supports this claim. From BBC.com, they say how Jack Sweeney uses public aviation records to see Taylor Swift's use of planes and how much her travels contribute to harmful emissions. "In a letter first revealed by the Washington Post, lawyers for the singer wrote that plane tracking was a "life-or-death matter" and there was "no legitimate interest in or public need for this information, other than to stalk, harass, and exert dominion and control"." Her team claims what he is doing to be an attempt to stalk and harass the singer, but Jack Sweeney's lawyers say, "The letter was an attempt to bully Jack into doing something that legally he doesn't have to do. Unfortunately folks with power and money often do this...He's not doing anything unlawful.""
https://www.bbc.com/news/world-us-canada-68248168