Delay spent the 2018 season with the High–A Bradenton Marauders, hitting .247/.325/.302 with two home runs and 21 RBI across 67 games.[8] In 2019, he played in 67 games for the Double–A Altoona Curve, slashing .234/.286/.398 with career–highs in home runs (8) and RBI (37). Delay did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[9]
He returned to action in 2021 with Altoona and the Triple–A Indianapolis Indians. In 30 games between the two affiliates, Delay batted .170/.204/.277 with two home runs and seven RBI.[10] He began the 2022 season with the Indianapolis Indians. In June 2022, Delay had decided he would retire from professional baseball during Indianapolis's upcoming trip to play the Gwinnett Stripers, near his hometown in Johns Creek, Georgia.[11][12]
On June 13, 2022, Delay was selected to the 40-man roster and promoted to the major leagues for the first time.[13] He made his major league debut on June 14 in the first game of a double header against the St. Louis Cardinals.[14] After going 0-for-2 with a walk in his debut, the Pirates optioned him back to Triple-A Indianapolis Indians.[15] On July 7, Delay recorded his first career hit, an RBI double off of Cincinnati Reds starter Mike Minor.[16] On July 22, Delay hit his first career home run, a solo shot off of Miami Marlins starter Braxton Garrett.[17] Delay made 57 appearances for the Pirates in his rookie campaign, hitting .213/.265/.271 with one home run and 11 RBI. He was outrighted off the roster on November 10.
On March 28, 2023, the Pirates announced that Delay had made the Opening Day roster as the backup catcher behind Austin Hedges.[18] He had his contract selected on March 30.[19] In 70 games for Pittsburgh, Delay batted .251/.319/.347 with one home run and 18 RBI.
Delay began the 2024 season with Pittsburgh, but played in only one game before suffering a knee injury. On April 19, 2024, it was announced that he would undergo surgery to repair a torn meniscus in his right knee.[20] He was activated from the injured list and optioned to Triple–A Indianapolis on June 3.[21]
On June 14, 2024, Pirates catcher Henry Davis was removed from the game after the 6th inning. Davis was placed on the 7-day injured list with a concussion. Delay was recalled from Triple-A Indianapolis on June 15, 2024.[22] He played his first game back the next day on June 16, 2024 and went 1-for-3 with a double and three RBI.[23]