Horne was one of the new inductees for season
2015–16 at the new
Scottish Rugby Academy as a Stage 3 player. Stage 3 players are assigned to professional clubs and Horne was assigned to
Glasgow Warriors. Horne made his debut for
Glasgow Warriors in a friendly match against the British
Army Rugby Union side on 25 September 2015. In a 71–0 victory for the Warriors, Horne came off the bench to grab a try. In November 2015, Horne was loaned to London Scottish, by Glasgow Warriors, to gain more experience of playing professional rugby. Horne remained as a Stage 3 player assigned to Glasgow Warriors in the
2016-17 season. He made his competitive debut for the Warriors in the
Pro12 match against the
Ospreys on 25 November 2016. Horne has an exceptional try scoring rate, averaging better than a try every other game at both club and international levels. In December 2024, he scored a hattrick of tries and three conversions in the opening round of the
2024–25 Champions Cup beating
Sale Sharks 38–19. On 29 March 2025, he broke the record of all-time try scorer for the Glasgow Warriors, beating the record set by
D. T. H. van der Merwe. == International career ==