Fourlis made her ITF debut in Glen Iris inMarch 2014. Her first win came in October 2014 in Cairns when her opponent Carolin Daniels retired while 0–3 down. In March 2015, Fourlis qualified for the Melbourne ITF tournament and made the semifinal. She played two more ITF tournaments in Croatia for the year. In 2016, Fourlis commenced the year at the Perth $25,000, where she qualified en route to winning her first title. She played a number of events across Australia and Great Britain, with limited success. She ended the 2016 season with a ranking of 427.
2017: Grand Slam debut
Fourlis was given a wild card into the Hobart International, where she lost to Kirsten Flipkens in the opening round. She made her Grand Slam debut at the Australian Open after winning the Wildcard Playoff. She defeated Anna Tatishvili before losing to Svetlana Kuznetsova in the second round. In February and March, Fourlis competed on the Australian ITF circuit, reaching the quarterfinals in Launceston. In May, she competed in Wiesbaden, Dunakeszi before winning an Australian wild-card play off into the French Open, losing to former world No. 1 Caroline Wozniacki in three sets. After the French Open, Fourlis took three months off to focus on her 'Year 12 studies', returning to the Australian ITF circuit in September, where she reached the quarterfinals in both Penrith and Brisbane. In December, Fourlis won the Under-18 Australian Championships and an 2018 Australian Open main-draw wild card.
2018: Top 200
Fourlis was given a wild card into the Hobart International where she defeated Nina Stojanović, before losing to Heather Watson in round two. At the Australian Open, she lost to Olivia Rogowska in the first round. In April, Fourlis won her second and third ITF titles. In June, her ranking peaked inside the world's top 200. Fourlis ended the year with a singles ranking of 202.
Fourlis is an offensive baseliner and has a powerful forehand which she uses to try to dictate play from the back of the court. Her backhand and serve are reliable. She covers the court well. When she plays, she looks to use her forehand to finish off points.