Jones started playing rugby at age 6, through mini rugby in her local club Ballymena RFC. There was no girls' rugby in her schools Cambridge House Grammar School and Ballymena Academy. Neve's attempts to launch it at both schools were rejected by the schools so she joined Malone RFC when she was 14.[1]
She captained the Ulster U18s to the first Irish U18 Provincial trophy in 2016.[2]
Jones was Malone's top try-scorer in 2019 and the winner of the 2020 Energia Women's All Ireland League Rising Star Award.Ulster under 18 player of the year.[3]
On 7 January 2022, Gloucester-Hartpury announced that they'd signed Jones to their squad.[4]
Before she played rugby she was involved in swimming, netball and jiu jitsu.[citation needed] She took up ladies gaelic football in 2020 and plays for East Belfast GFC, the first GAA team to be set up there in nearly 50 years.[8]