Gaulden attended Independence High School in Thompson's Station, Tennessee. Along with football, he also participated in track and field and was named an All-American after finishing fourth nationally in the 4x400 relay. During his senior football season, he recorded 193 tackles. Gaulden committed to play football for the Tennessee Volunteers on July 20, 2013, choosing the Volunteers over programs such as Vanderbilt and South Carolina.
As a true freshman in 2014, Gaulden played in 11 games, making seven total tackles.
Gaulden missed the 2015 season due to a foot injury suffered during training camp in August and took a medical redshirt.
Gaulden returned in 2016 as a redshirt sophomore and played in all 13 of Tennessee's games, recording 68 tackles (six for loss), four pass breakups and one forced fumble.
As a redshirt junior in 2017, Gaulden played in all 12 games of the season, tallying 65 tackles, one interception, five pass deflections and three forced fumbles. After the season, he declared for the 2018 NFL Draft.