Moodie's first television role was in the comedy So Haunt Me in 1994, followed by a starring role as Hunter in Neil Gaiman's 1996 fantasy mini-series Neverwhere (1996). She featured in guest roles in various series in the 2000s, and in 2008-9 had a regular role in Irish medical drama The Clinic. More recently she played the role of John Watson's therapist Ella Thompson on Sherlock.

In 2016 she played Gertrude in Simon Godwin's production of Hamlet for the Royal Shakespeare Company.

Tanya was nominated for a 2017 UK Theatre Award for Best Performance for her performance as Wiletta in 'Trouble In Mind'. Other nominations include Best Actress at the London Evening Standard Theatre Awards, as well as an Olivier for Outstanding Achievement in an Affiliate Theatre for her performance as Esther in Intimate Apparel at the Park Theatre. That same year she was also nominated for an Olivier for Outstanding Achievement in an Affiliate Theatre for her performance as Makeda in The House That Will Not Stand at the Tricycle Theatre. Her portrayal of Rose in August Wilson's 'Fences' opposite Lenny Henry in the West End earned her a nomination for Best Actress in the 2014 What's On Stage Awards. Her many stage credits include productions with The Royal Shakespeare Company, The Royal Court Theatre, The National Theatre and the Bouffes Du Nord in Paris where she spent a year working with Peter Brook, touring with his production of 'Le Costume'.