Simmons, 20, came off the bench to make his fourth first-team appearance in the Anglo-Welsh Cup victory over Cardiff Blues at Welford Road. It followed his European debut as a replacement in the Champions Cup game at Castres Olympique.
White, 19, meanwhile, became the youngest Tiger to play in Premiership Rugby when he made his Leicester debut as a 17-year-old in October 2015. He is now on international duty with England U20s as they prepare for their Six Nations campaign, which kicks-off against Italy on Friday.
And the pair say that Ben Youngs and Sam Harrison are the perfect players to help them learn their trade.
“From a progression point of view, there is no better club to be at,” said White. “The nines that we have here are the best in the world. It’s great to be around that environment and around that quality, and learning off that.
“Me and Harry are training together all the time. It’s good to push each other and try to get the best out of each other.”
Simmons added: “It’s brilliant having Ben Youngs and Sam Harrison to learn from. They help us out loads, and me and Whitey are always pushing each other to get better. We are always striving to be better.”
A member of the Norfolk contingent in the academy, Simmons describes playing rugby for Tigers as “a dream job”.
“It was a great experience to play in Castres,” he said. It was a disappointing game but it was nice to make my debut – even if I did get a nice scar for it too.
“Steve Mafi came off the back of a lineout, I dived for him and caught his boot as it came up. He has size 16 boots so it’s difficult to miss them!
“I have loved the experiences. It’s a dream job.”
White echoed his teammate, saying it was a privilege to play for the club.
“I have always wanted to play for Leicester since I was young,” he said. “The chance to extend that chance of playing for the club, it was an easy decision for me to make.
“To play for Leicester is something that I’ve always wanted to do and to have the chance to do that is a privilege to be able to do it.
“Having played a couple of times, you get that taste of it and you want more. I am looking forward to trying to push to play more games and to get as much experience as I can.”