Following the completion of GCSE exams Burrage relocated to Junior Tennis Coaching (JTC) in Chiswick, London, where she was guided by former tour professionals Colin Beecher and Lucie Ahl.

[23] She reached the quarterfinals at the Stanford WTA Challenger, beating Diana Shnaider[24] and Kayla Day,[25] before a narrow three-set loss to Moyuka Uchijima.

[30][31] Burrage captured her maiden WTA Tour title winning the doubles with Jil Teichmann at the 2023 Transylvania Open, defeating Léolia Jeanjean and Valeriya Strakhova in straight sets in the final.

[32][33] She made her debut for Great Britain's Billie Jean King Cup team in November 2023 in a play-off tie with Sweden held indoors at the Copper Box Arena in London.

[36] At the Linz Open in Austria, she came through two qualifying rounds and then beat Varvara Gracheva[37] and Jaqueline Cristian[38] to reach her first WTA 500 event quarterfinal, before losing out to Jelena Ostapenko.

[40] After recovering from the surgery, Burrage was set to return to action at the French Open in May for what would have been her first main-draw appearance at the clay-court event, but she was forced to pull out just days before the tournament began when she injured her ankle in practice.

[42] Having missed six months of the season, Burrage returned to the competitive court in September in the qualifying stages at the Jasmin Open in Tunisia, winning her first match against Lina Soussi in straight sets.

[46] The following week, having received a wildcard entry, she went one step better, winning the biggest title of her career to date at the W100 Al Habtoor Tennis Challenge in Dubai, defeating top seed Polina Kudermetova in the final.

[49] Burrage started her 2025 season at the Auckland Open where she entered the main draw as a lucky loser and defeated wildcard entrant Vivian Yang in the first round,[50] before losing her next match to Hailey Baptiste in a deciding set tiebreak.

[51] Using her protected ranking to gain entry into the main draw at the Australian Open, she defeated qualifier Léolia Jeanjean to reach the second round,[52] where she lost to third seed Coco Gauff.