Much like his compatriot Casey Stoner, Arthur honed his talents in state and then national competitions, debuting on the 125cc speedway scene at just nine years old. He continued to collect domestic titles all the way through the categories before a change of tack.
As Arthur cleaned up on his home scene, his delving into road racing brought an invitation to compete in the Red Bull MotoGP Rookies Cup in 2009. He stayed on the following season and finished 13th overall.
In 2011 Arthur battled for the Rookies title right down to the final race, eventually finishing runner-up. His displays earned him a ride in the 125cc class at the Malaysian Grand Prix, where he stood in as a replacement rider, and shortly after he was confirmed as a full-time entry for the Red Bull KTM Ajo team in 2012, for whom he made his World Championship debut in Moto3.
It was a season packed full of promise, as Arthur took a top-five finish in Le Mans in only the fourth round, and a first podium in his home GP in Australia towards the end of the campaign highlighted his huge promise. He stayed with the team for 2013, but wasn't able to replicate the form of the previous season. In 2014 Arthur switches to Mahindra Racing, staying in Moto3 to challenge for the top with the Indian manufacturer.