There’s a piece of the new state budget that’s under the radar right now, but could have big implications for New York City.

In 2013, neighboring Nassau County won approval to operate 1,000 video lottery terminals — but no neighborhood wanted them. So a deal was made last week to put the machines at Aqueduct’s Resorts World Casino and send a big check to Nassau. That clears the way for grander plans at the Queens track and at nearby Belmont Park.

Genting New York LLC already operates about 5,400 gambling machines at Aqueduct. With this move, Genting gets the new machines and avoids a rival gambling operation just a few miles away. Having VLTs at both Aqueduct and Belmont, about 10 miles from each other, wouldn’t have been good business. Having two thoroughbred tracks so close to each other hasn’t worked so well, either.

Aqueduct is a timeworn, utilitarian horse track. Belmont is grander, with a storied history and tremendous upside. It would make sense to move all horse-related activity out of Aqueduct and over to a new winterized track at Belmont, as the New York Racing Association wants to do.

This would allow Genting to clear out space to be a full casino with table games in New York City; it could be the busiest in the world. In that scenario, Genting would likely have to give NYRA money to redevelop Belmont.

To thrive, Belmont will need a re-imagining that includes food and entertainment and a modern, rebuilt Long Island Rail Road train station. That, in turn, would give eastern Queens neighborhoods a direct rail link to Manhattan.

Making Belmont a year-round racing and entertainment center also could open up possibilities for 28 acres of undeveloped state-owned on the south side of Belmont Park. And it could give the area around Aqueduct another shot at revitalization.

These plans would take years to unfold. All of them must have deep involvement of local planning boards and local officials. Aqueduct and Belmont and their neighborhoods could get a shot at a better future.

This bet has to be a win for everyone.