Gilman played his freshman year at the United States Naval Academy. He played in all 14 of the Midshipmen's games and was named honorable mention All-American Athletic Conference after finishing second on the team with 76 tackles along with five passes defended and two fumble recoveries.[2] Gilman transferred to Notre Dame after his freshman year.[3]
Gilman sat out his sophomore year per National Collegiate Athletic Association (NCAA) transfer rules. As a junior he started 13 games and finished the season with 95 tackles, three tackles for loss, and three forced fumbles, with two interceptions with five passes broken up.[4] He was named a team captain as a senior and recorded 74 tackles, three tackles for loss and one sack with one interception, two passes broken up, one fumble recovery and three forced fumbles.[5] After the end of season, Gilman announced that he would forgo his final year of NCAA eligibility to enter the 2020 NFL draft.[6]
The Los Angeles Chargers selected Gilman in the sixth round (186th overall of the 2020 NFL draft. Gilman was the 15th safety drafted in 2020. He was reunited with former Notre Dame teammate Drue Tranquill who suggested to Los Angeles Chargers staff to draft Gilman.[9]
After playing almost exclusively on special teams as a rookie, Gilman contributed on defense the next two seasons as a third safety. He was named the starting free safety for the 2023 season, starting 14 games while recording 73 tackles, three forced fumbles, and two interceptions.
On March 13, 2024, Gilman signed a two-year contract extension with the Chargers.[10]