Chalmers played with James the last four seasons in Miami and was often on the receiving end of criticism from the four-time MVP.
"LeBron is a dominant player so if he feels like something is not going his way, he's going to say something about it," Chalmers told Northeast Ohio Media Group. "For Kyrie, he's going to have to adjust to that and LeBron is going to have to adjust to Kyrie. It's going to be a different factor for Kyrie."
Irving averaged 20.8 points and 6.1 assists last season while attempting 17.4 shots per game as Cleveland finished 33-49. James left the Heat after four straight appearances in the NBA Finals to return to the Cavaliers.
Irving, who injured his right ankle earlier this week, was named the MVP of the 2014 FIBA World Cup last month.
Earlier in the week, Heat forward Chris Bosh said it will be "very difficult" for Cavaliers forward Kevin Love to adjust to playing with James as the first option on offense. Bosh said Love will have to "fight a lot of his instincts."
The Cavaliers and Heat play on Saturday in Brazil as part of the NBA's Global Games. Cleveland opens the regular season on Oct. 30 against the New York Knicks. The first regular season game between the Cavaliers and Heat will be on Christmas Day in Miami.
- Paul Palladino