[8] Grier was offered scholarships to play football at Auburn, Arkansas, Florida, North Carolina, Tennessee, and Wake Forest.

[9][10] Grier competed with Treon Harris to be Jeff Driskel's backup as a freshman in 2014, ultimately redshirting the season.

Although Harris started the first game of the season against New Mexico State, Grier received playing time, attempting 18 passes and completing 16 for 166 yards with two touchdowns.

[12][13][14] On October 3, against the Ole Miss Rebels, he had the best game of his young career, going 24-of-29 for 271 yards and four passing touchdowns.

Grier received a one-year suspension, effective October 12, 2015, after it was revealed that he had tested positive for performance-enhancing drugs.

He said the positive test stems from the drug Ligandrol, and that he was not aware it was banned, while also admitting he never followed protocol to clear the supplement with team trainers.

Grier was the presumed starter for West Virginia heading into the 2017 season, but there were questions surrounding his eligibility, since half of his year-long suspension was served in conjunction with his transfer waiting period.

[21] In his first game with the Mountaineers, Grier threw for 371 yards, three touchdowns and an interception in a 31–24 loss to Virginia Tech.

[23] Grier had surgery on the broken finger and missed the remainder of the season, finishing with 3,490 passing yards and 36 total touchdowns on the year.

[39] In Week 17 season finale against the New Orleans Saints, Grier threw for four yards and a pick-six before exiting the game due to a foot injury in the second quarter.

[40] In 2020, new head coach Matt Rhule signed free agent Teddy Bridgewater to be the starter at quarterback.

[41] On September 1, 2021, Grier was claimed off waivers by the Dallas Cowboys, to replace Ben DiNucci as the third-string quarterback behind Dak Prescott and Cooper Rush.

[52] He was acquired to be the backup behind Easton Stick, who took over the quarterback starting job after Justin Herbert was placed on injured reserve with a broken finger.

[58][59] He has two brothers, Nash and Hayes, a half-sister, Skylynn Elizabeth Floyd and a half-brother, John Henry "Hank" Grier.

[60] Nash, Hayes and Skylynn were popular users of Vine, the defunct video sharing service.