Leeming has taken over from Matt Prior, who skippered the side over the second half of last year after Luke Gale had the role taken away following a bust up with coach Richard Agar.
Handley has had occasional games as captain of his hometown club, but insisted Leeming is a “great” appointment.
The hooker joined Rhinos from Huddersfield Giants ahead of the 2020 season and was their only player selected in last year’s Betfred Super League Dream Team.
He also made his England debut in 2021 and Handley said: “He leads by example.
“I think when he speaks, people do listen to him.
“His opinion is respected by everyone in the club and it will only do him favours.
“It will give him the confidence to push his game on further.”
Leeming will captain Rhinos in a competitive game for the first time when Warrington Wolves visit Headingley a week tomorrow in Super League round one.
Of his own new role, Handley said: “I‘ll be there when he needs me and try to lead by my actions and help in any way I can.”
Handley, who turns 26 later this month, is one of the club’s longest-serving players, having made his debut in 2014.
He admitted it is “strange” to be in that situation at a relatively young age, but stressed he is making up for lost time following two seasons disrupted by the pandemic.
“I feel like Covid has taken a couple of years away from us,” he said.
“When you’re playing behind closed doors, it’s almost like people don’t get to know you personally.
“It’s like I’ve had four or five years playing and it’s taken the sixth and seventh year off me.
“I am just looking forward to packed out stadiums and playing rugby and just growing now.
“Hopefully we can put all the Covid stuff behind us and the sport can grow and grow and get back up there now.”
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