The forward, 20, has signed a one-year contract extension for 2022.
Peachey came through the club's academy system and debuted against Catalans Dragons two years ago.
Equally adept at prop or second-row, he made seven appearances this term.
"I am really happy to be staying," he said.
"With a new coach coming in next year, I am hoping to push on and hopefully get some more game-time.
“I got a few games this year, probably more than I thought and I am hoping to get the same or even more next year.
“I came through the TTP (Tigers Talent Pathway), then the Scholarship and Academy so it is all I have known really. It is good to be staying and I can continue to improve.”
Fellow young forwards Sam Hall and Brad Martin also recently inked new deals while, at 22, Jacques O’Neill is another player looking to make his mark as Lee Radford takes over.
Peachey said: "Me and some of the younger lads were able to get some good experience this year and hopefully I can take that and improve next year.
“All the youngsters coming through are a good bunch of lads to compete with and we are all aiming for the same goal so hopefully we can all make plenty of appearances.”
Radford said: "Lewis is a good kid and the games I have watched him in this year, he has been tidy.
“The likes of him and Sam Hall have played a lot together when they have come into the First Team and to give them an opportunity, but with more senior players around them, will be great for their development.”