She appeared as Katie Burrell, the daughter of a Japanese relocation camp sergeant, in the 2007 film American Pastime.

She later guest-starred on Cold Case, Law & Order: Special Victims Unit, Medium, Castle, Glee, Privileged, Supernatural, and Private Practice.

[7][8] She starred in the Hallmark Hall of Fame film Front of the Class (2008), and from 2008 to 2009, she had a recurring role as Kitty Romano in the AMC drama series Mad Men.

[20] In July 2018, Drew took on the role of Lucille Ball, starring in the world premiere production of I Love Lucy: A Funny Thing Happened on the Way to the Sitcom, a behind-the-scenes stage comedy about I Love Lucy by Gregg Oppenheimer (son of series creator Jess Oppenheimer).

Recorded before a live audience at the UCLA's James Bridges Theater, the L.A. Theatre Works production aired on public radio and has been released on Audio CD and as a downloadable MP3.

[25] On October 30, 2020, Drew has been cast in a recurring role as Cindy Turner (Jeanette's mother) in the Freeform (ABC Family) series Cruel Summer.

[26] In September 2021, Drew was cast in Apple TV+ comedy series Amber Brown based on the bestselling books by Paula Danziger.

[27] In 2022, Drew started as Lizbeth Meredith in the Lifetime movie Stolen By Their Father as part of its "Ripped from the Headlines" feature films; it had Elizabeth Smart as an executive producer.