Rhea Clarke began playing rugby at Dunfermline RFC when she was six-years-old alongside her sister, Ellian, who is also a Scotland Women international.

The scrum-half moved onto Stirling County where she was part of the team who raised the U15 Cup in 2017 and U18 Cup in 2018 and 2019. 

During the 2019/20 and 2020/21 seasons, Rhea was selected for Scotland U18, playing in the U18 Six Nations festivals. 

Rhea began studying at the University of Edinburgh and joined the rugby team in 2021. In the same year, she and the squad reached the 2021/22 BUCS Cup final.

In the following season, Rhea was a Player of the Year nominee in the BUCS league, and in 2023/24 she won the BUCS Keri Holdsworth Award.  

During 2022 and 2023, Rhea was selected for The Thistles in the inaugural Celtic Challenge and was selected to represent Scotland Futures. At the same time, she was invited into training camps with Scotland Women in preparation for the Rugby World Cup, Six Nations 2023 and the Six Nations in 2025.

In the 2023/24 season, Rhea was named as the co-captain of Glasgow Warriors in the Celtic Challenge, making seven appearances. In the 2024/25 season, she was drafted to Edinburgh Rugby.

She made her Scotland Women debut against England in round four of the 2025 Guinness Six Nations, playing alongside her sister, Elliann. Rhea was part of the squad for the Rugby World Cup squad that year.

After a spell with Bristol Bears in the PWR, she signed for Glasgow Warriors ahead of the 2026/27 Celtic Challenge season.

Away from rugby, Rhea has excelled in other sports, playing hockey, basketball and judo. She was also the Scottish National at U14 level in vaulting.