Born in Hobart, Tasmania, Morice also lived in Sydney, Alice Springs and Adelaide as a child.

Morice has also appeared in the feature films Metal Skin, Hotel Sorrento, Hildegarde, Moulin Rouge!, Candy, Razzle Dazzle: A Journey Into Dance, Oranges and Sunshine, Dance Academy: The Movie and Peter Rabbit 2.

Her television work includes roles in Answered by Fire, After the Deluge, Salem's Lot and McLeod's Daughters.

Tara played Shell in the premiere of the Australian musical The Deb at the Rebel Theatre in Sydney 2022 and in The Deb directed by Rebel Wilson, its World Premiere slated for closing night at the 2024 Toronto International Film Festival.

In 2024 Morice was named in the cast for Stan Australia feature film Nugget is Dead.