The Nets and Caris LeVert reached a contract extension Sunday, one that should keep Brooklyn’s rising young guard a big part of their playoff core.

The three-year, $52.5 million extension — first reported by ESPN and confirmed by The Post — came on LeVert’s 25th birthday.

“No better feeling to start off Year 25. Brooklyn, I can’t wait for what’s next,” LeVert tweeted, along with a video montage of his days with the Nets. “Brooklyn: This is always where I wanted to be…This is where I started my career and this is where I want to continue it.”

LeVert — who averaged 13.7 points, 3.9 rebounds and 3.8 assists in a season interrupted by a gruesome foot injury — is still on his rookie deal for this upcoming campaign. The rookie extension — which was largely expected — won’t kick in until the 2020-21 season.

After the Nets added Kevin Durant, Kyrie Irving and DeAndre Jordan — doling out over a third of a billion dollars worth of contracts — LeVert’s deal signals new owner Joe Tsai is willing to pay to win, even if that includes luxury tax. LeVert has flashed All-Star potential and could have the upside of a third star on a championship team.

Considering that level has recently included the likes of Klay Thompson, Kevin Love and Chris Bosh, that’s a tall order. But LeVert may have that kind of ceiling if he can stay healthy. That’s why this contract protects both him and Brooklyn.

Before going down Nov. 12 in Minnesota, LeVert was averaging a team-high 18.4 points and getting early All-Star buzz. He missed 42 games and took awhile to get back on track. But he averaged 16.0 points over his final eight games in the regular season and was far better in the postseason.

The Nets’ best player at the beginning of the season, LeVert was again at the end. He poured in a team-high 21.0 points in the playoff series against the Sixers — second in the series behind only Philly’s Joel Embiid.

That kind of talent promoted Spencer Dinwiddie to posit that LeVert could be a 20-point scorer.

“Honestly, it’s hard to say. He’s definitely talented enough to average 20,” Dinwiddie said in a video on social media. “It’s going to kind of all depend on how the team comes together, how roles are defined, what happens once KD comes back — I guess probably next season right? — and seeing how it all comes together. But he’s definitely talented enough and capable enough to be a 20-point scorer in the NBA.”

That seems to be what the Nets are banking on. If LeVert did that this season, going into restricted free agency, they would’ve faced the prospect of having to pay even more to keep him.

Foot problems at Michigan caused him to drop to the Nets at 20th overall back in 2016, as GM Sean Marks’ first-ever draft pick. And since his junior season with the Wolverines, he’s logged respectively 18, 15, 57, 71 and finally 40 games. Now he has guaranteed money as a fallback in case he gets hurt again — and the Nets have a potential elite talent if he doesn’t.

As is his custom, Marks snuck a poison pill provision in LeVert’s contract for this season. His outgoing salary would count as only $2.6 million, the final year of his rookie deal. But his incoming salary would count a more daunting $13.8 million according to ESPN, the average of this year’s salary and the extension.