Donald Trump is poised to run away with next week’s Republican primary in New York, a new Wall Street Journal/NBC New York/Marist poll shows.

The New York businessman leads his closest rival, Ohio Gov. John Kasich, by 29 percentage points among likely Republican primary voters, 54% to 25%, the poll finds. Texas Sen. Ted Cruz is a distant third, as the top choice of 16% of likely Republican voters.

The...