From 1994 to 1996, she was an assistant appellate defender in the State Appellate Defender's Office. From 1998 to 1999, she was an associate attorney with Kohn & Einstein in Washington, D.C. From 1999 to 2003, she worked at the Alexandria Public Defender's Office in Alexandria, Virginia. From 2003 to 2005, she was an associate attorney with Damiani & Damiani, P.C in Alexandria, Virginia and from 2006 to 2012, she was a staff attorney with the St. Cloud Area Legal Services of St. Cloud, Minnesota.[3]
In April 2024, Hennesy was one of six candidates named for possible appointment to the Minnesota Supreme Court.[6] On April 22, 2024, Governor Tim Walz announced the appointment of Hennesy to the Minnesota Supreme Court. She was appointed to the seat vacated by the retirement of Justice G. Barry Anderson.[2] Hennesy assumed office on May 13, 2024.[3] Governor Waltz also announced the appointment of Judge Theodora Gaïtas to fill the upcoming vacancy created by the retirement of Justice Margaret Chutich.[2] With their appointments, the court will return to a female-majority since the retirement of Justice Rosalie E. Wahl in 1994.[7]