EAST RUTHERFORD, N.J. -- It won't take long for Leonard Williams to get an opportunity to show the New York Jets they made a mistake by trading him to the crosstown rival New York Giants.

The former No. 6 overall pick for the Jets admits there is a "little extra juice" for the game against his former team Sunday (1 p.m. ET, Fox). Giants vs. Jets means something, especially with both teams so desperate for a victory.

Williams not only gets to play against his former team, but will do so in a prominent role that has Giants defensive coordinator James Bettcher staying up at night dreaming of ways to maximize his newest lineman's potential. The Giants believe they can get Williams to become the player the Jets envisioned when they selected him in the first round (No. 6 overall) of the 2015 NFL draft.

"I think one thing we need to do is keep trying to find ways to get him one-on-ones," Bettcher said. "He had a couple really nice one-on-one pass-rush wins in that [Cowboys] game [Monday night]."

It should be no surprise that the Giants are all-in on trying to maximize Williams' talent. They traded a third-round pick in 2020 and fifth-rounder in 2021 to get their shot at him before free agency next spring.

But they also know there is work to be done. Improving his pass-rush arsenal appears to be a priority.

"The thing that him and I have talked about in his one-on-one pass-rush stuff is building his counter, what is his pass-rush counter?" Bettcher added. "This is a guy when you watch him, he rushes long, and he plays as tall as he is and as long as he is. Not all long guys do that."

Williams had a mixed debut for the Giants on Monday night against the Dallas Cowboys. He had five total pressures (1 QB hit, 4 pressures) but finished with a 48.8 overall grade, according to Pro Football Focus.

But Williams won't be facing the All-Pros that Dallas boasts in the middle of its offensive line. The Jets don't have anywhere near the same level line. In fact, they are on the other end of the spectrum, providing a golden opportunity for Williams to showcase his talents in an attacking scheme that might suit him perfectly.

The way the Jets were utilizing Williams had him facing constant double-teams. He had faced the seventh-most double-teams in the league before coming to the Giants, according to Next Get Stats.

It has become a priority for Bettcher to limit that in his scheme.

"Definitely excites me," Williams said. "It shows me that they're excited about me and they value what I bring to the table. They want to set me up with as many good opportunities and matchups for me. That speaks volumes on the staff and me as well, and I have to prove to them why they should keep doing that."

Williams had a 13.6 percent QB pressure rate percentage in his first game with the Giants. He had a 6.8 QB pressure rate in his eight games with the Jets. It's a small sample size but it's at least a solid start toward becoming the player the Giants envisioned when they made the trade.

The Giants' scheme had Williams facing a double-team (which is much more common on the interior of the defensive line than on the edges) on 10 of 41 snaps against the Cowboys.

"I obviously don't want to make excuses," Williams said. "Everyone gets double-teamed, especially good players in the league. I have to be able to beat double-teams as well. That is just the nature of the game. Just keep working hard and keep staying at it, keep staying persistent is what is going to make it get past that hump."

This week he'll be facing a beleaguered Jets line that has allowed 37 sacks, second only to the Tennessee Titans, who have played an extra game. It's a group he's familiar with, having practiced against them regularly.

It's a quarterback he's quite familiar with as well, having played with the Jets' Sam Darnold for the past two years. But this is Williams' chance to finally hit him -- unless his habit of not hitting Darnold takes over.

"I actually randomly thought in my head, 'what if I beat somebody and go to tackle Sam and I let up because I can't hit him?'" Williams joked Thursday. "Nah, that won't happen. I finally get to tackle him. That will be fun. It will be great."

It will be great for the Giants if that opportunity even presents itself. They made the trade in part because they were desperately looking for an impact defensive player.

Williams, a good-but-not-great player with the Jets, could immediately be the Giants' best player on a talent-deficient defense. The opportunity to excel might just be what he was looking for with free agency or a new contract on the horizon.