Neely attended Winston Churchill High School in San Antonio, Texas and played college baseball at the University of Texas at Austin, Iowa Western Community College and Ohio State University.
[1] The New York Yankees selected Neely in the 11th round, with the 333rd overall pick, of the 2021 Major League Baseball Draft.
Neely split the 2022 season between Tampa and the High–A Hudson Valley Renegades, accumulating a 3.58 ERA with 87 strikeouts and 7 saves across 38 relief outings.
[3] In 2023, Neely played with Hudson Valley and the Double–A Somerset Patriots, registering a combined 6–5 record and 2.17 ERA with 100 strikeouts and 7 saves over 42 games out of the bullpen.
On July 30, 2024, the Yankees traded Neely and Ben Cowles to the Chicago Cubs in exchange for pitcher Mark Leiter Jr..[5] He made six scoreless appearances for the Triple–A Iowa Cubs, striking out 13 batters and recording three saves.