New head coach Dave Rennie took over at Scotstoun on Monday and has told the full-back he will have to earn his jersey.
Speaking to BBC Scotland, Stuart said: "He just said that reputations go out the window and it's all about hard work - and, for me, that's right.
"We've got reputations that are all in the past - we're in control of what happens in the future.
"Everyone has a hard work ethic at Scotstoun and that's what drives us on to become better every year.
"All the international boys have only been in two or three weeks - boys have done the full block of pre-season, they're in unbelievable condition.
"It's not just a case of slotting back into the team - we're going to have to earn it. But that's very much what happens at Glasgow Warriors."
A facial injury forced the 25-year-old premature withdrawal from this summer's British and Irish Lions tour of New Zealand before he had an underlying shoulder complaint operated on during June.
He and lock Jonny Gray, who had injured a wrist, were at that time given recovery periods of between four and six months, but Stuart was non-committal on the prospect of the pair returning for Glasgow's opening European Champions Cup pool matches in October.
"We've got the timescale that we'd like to be back for and, for me, that will remain in-house," said Stuart.
"We're very much on-target and we'll keep working hard and try to hit our daily and weekly targets.
"But it's not an injury I'm going to come back from in no time - it's going to take a lot of time, effort and hard work - and I want to be in a position where I'm getting the best out of myself.
"I'm not going to come back at 80-85%, I want to be 100% and I'm very excited to get back on the pitch."
Dave Rennie's appointment marks a period of major upheaval at Scotstoun, with 11 new players signed and former Scotland assistant coaches Jason O'Halloran and Jonathan Humphreys joining from the national side.
Stuart, who signed a new two-year Warriors deal in October, said: "For us to get a guy of Dave Rennie's calibre and Jason and Humphs, cracking coaches, it does feel like a new club coming in over the last few weeks.
"But it's the same players, we all know how each other play, it's just a case of buying into the way Dave wants to play.
"For us, it's exciting times. We had a couple of chats over here, he came over to see how everything was working and he was hugely key to me staying on at Glasgow again.
"I've heard nothing but good reports about him. I've got a lot of time for him already."