[1] Greaves was part of the Junior Olympic Program and competed with her mother's gym, Athletic Edge Sports Center.

Greaves began training at MG Elite Gymnastics and competed level 8 during the 2015 season, the same gym as rising junior Laurie Hernandez.

In 2016 she competed at the Level 9 New Jersey State Championships where she finished first in the all-around, vault, and uneven bars, second on floor exercise, and tenth on balance beam.

At the 2017 Level 10 New Jersey State Championships, Greaves finished first in the all-around, on vault, and on floor exercise, second on uneven bars, and third on balance beam.

[4] In early July, Greaves competed at the American Classic where she placed fourth in the all-around behind Kayla DiCello, Konnor McClain, and Skye Blakely but first on the uneven bars.

[10] While there she helped the USA win team gold and won silver in the individual all-around behind Canadian Zoé Allaire-Bourgie.

Individually she qualified to all four event finals and won silver on vault and floor exercise, behind Blakely and Allaire-Bourgie respectively, and placed fifth on uneven bars and balance beam.

[16] Greaves was unable to compete at the 2021 National Championships or the Olympic Trials due to elbow fracture diagnosis, which later turned out to be a bone bruise.