After several appearances in regional theatre productions and minor roles in short films and television episodes, Laurence auditioned for the new musical Matilda on Broadway in 2012.

After Matilda, Laurence transitioned to film acting, appearing in Tumorhead, A Little Game, The Grief of Others, I Smile Back, Damsel, Lamb, and Southpaw, portraying the daughter of Jake Gyllenhaal and Rachel McAdams' characters.

In 2017, Laurence co-starred opposite Colin Farrell, Nicole Kidman, Kirsten Dunst, and Elle Fanning in Sofia Coppola's The Beguiled.

She is the voice of Hedgehog and additional characters in the Cartoon Network series Summer Camp Island.

In 2020, she starred in the Netflix American family dark fantasy film A Babysitter's Guide to Monster Hunting alongside Tom Felton, Indya Moore, and Tamara Smart.