[10] After playing the early rounds of the Tom Kirby Memorial Irish Matchplay in Tramore, Barry qualified for the final which was contested during the 2019 World Grand Prix in October.

[11] In the lead-up to the match, he claimed his first BDO senior title at the Northern Ireland Matchplay with a 6–2 victory over Paul Hogan.

[14] On 16 December 2019, Barry made his PDC World Championship debut as the youngest player in the tournament at age 17, but lost to Vincent van der Voort 3–0 in sets.

On the last day of play, he reached the final where he faced Scott Waites with the victor obtaining a Tour Card; Barry lost 5–0.

[24] He got past Thomas Lovely and Dirk van Duijvenbode to reach the third round, where he lost to eventual runner-up Michael Smith.

[27] At the 2022 UK Open, Barry had his best run at a PDC major event by reaching the semi-finals, including eliminating the defending champion James Wade 10–4 in the quarter-finals.

[30][31][32] Barry was eliminated in the first round of the 2023 World Championship, suffering a shock 3–1 loss to South African qualifier Grant Sampson.

[36] Barry also represented Ireland in the PDC World Cup of Darts for the first time at the 2023 edition, partnering William O'Connor.

[39] In November, Barry was one of eight players to earn a place at the 2024 Grand Slam of Darts through the Tour Card Holder Qualifier, making his debut at the event.

[40] He finished third in Group F with a win against Lourence Ilagan and losses against Luke Littler and Dimitri Van den Bergh.