Narron was also a coach for Team Israel, under manager Ian Kinsler, when it competed in the 2023 World Baseball Classic.

[1] His father John was employed as a salesman and floor layer for the Isaacs-Kahn Furniture Company in Goldsboro.

He attended Goldsboro High School, where he played baseball, basketball, and football, and graduated in 1974.

Narron was a manager in the Baltimore Orioles farm system from 1989 through 1992; of the Single–A Frederick Keys (1989), Double–A Hagerstown Suns (1990-91), and Triple–A Rochester Red Wings (1992), with a record of 291-269 (.520).

Narron then served as bench coach for the Boston Red Sox during their 2003 run to the American League Championship Series.

On February 25, 2008, Narron was named a special assignments scout and front-office consultant with the Rangers.

[14] After the first seven games of the 2017 season, Narron took over as interim bench coach of the major league Arizona Diamondbacks, when bench coach Ron Gardenhire left the team on a leave of absence to have and recover from prostate cancer surgery.

[18] On February 10, 2021, Narron was hired as a major league instructor for the Chicago White Sox.

[23][2][25][26] Narron was again a coach for Team Israel, under manager Ian Kinsler, when it competed in the 2023 World Baseball Classic.

[5] He has five children and two stepchildren: Connor, Cara, Clare, Caitlyn, Callie, Chelsy, Coco and Hunter.

His son Connor was the fourth-ranked prospect for the high school class of 2010 by ESPN's Perfect Game.

The Orioles selected Connor in the fifth round of the 2010 MLB draft; he played in Minor League Baseball during the 2010 to 2014 seasons.