Clinch grew up in the village of Ranelagh in Dublin.[1] Her father, Tom Clinch, is a stockbroker, and her mother is the singer Méav Ní Mhaolchatha.[1][2] She took acting classes from a young age.[3]
Clinch first appeared on screen in Colm Bairéad's The Quiet Girl (An Cailín Ciúin) as Cáit, a reserved 9-year-old who spends the summer of 1981 on a distant relative's farm.[1] Auditions were sought for a lead actress who could speak Irish, the language of most of the film, and the role at Irish-language schools during the COVID-19 pandemic.[1] The film's producers recalled deciding quickly that Clinch was right for the role—able to carry the film—when they saw her audition tape.[3][4][5][6] Shot in 2020 and released in 2022,[7][8] the film was critically acclaimed alongside praise in particular for Clinch's performance.[9][10] She was commended for conveying "a deep reservoir of emotions" while showing studious restraint.[11][12] She was awarded Best Actress in a Leading Role for The Quiet Girl at the 18th IFTAs.[13]