Robinson became active in the movement for expanded rights for gays and lesbians, and served as co-counsel in the case of Baker v. State, the 1999 decision that led to Vermont passing the first civil unions law.

After working on Peter Shumlin's successful campaign for governor in 2010, Robinson joined his staff as legal counsel, a position which included drafting and analyzing proposed legislation and regulations, making recommendations on whether to approve requests for pardons, and ensuring compliance with ethics rules.

[7] In 1986, Robinson received her Bachelor of Arts degree in philosophy and government from Dartmouth College, and she graduated summa cum laude and Phi Beta Kappa.

[18] Robinson was employed for 18 years at Langrock, Sperry & Wool, a law firm with offices in Burlington and Middlebury.

[17] While there, she worked on issues of workers' compensation, personal injury, constitutional law and, most prominently, gay and lesbian rights.

[20] She was subsequently involved in the 2009 legislative battle to enact same-sex marriage, chairing the Vermont Freedom to Marry advocacy organization and working closely with Peter Shumlin, a prominent supporter of same-sex marriage, who was then President pro tempore of the Vermont Senate.

[24] Robinson was active in Shumlin's successful 2010 gubernatorial campaign, then joined his administration as his general counsel.

[17] On October 18, 2011, Shumlin announced he was appointing Robinson to the Associate Justice's seat on the Vermont Supreme Court that had been vacated by Denise R. Johnson's retirement in August 2011.

[29] Her service terminated when she resigned after being confirmed as a judge on the United States Court of Appeals for the Second Circuit.

[31] President Biden nominated Robinson to the seat vacated by Judge Peter W. Hall, who assumed senior status on March 4, 2021.

[33] During Robinson's confirmation hearing, she faced questioning from Republican Senators over her views on religious freedom.