The recent NY Times article Neptune’s Moon Triton Is Destination of Proposed NASA Mission says (in part):
HOUSTON — Is it time to go back to Neptune?
Scientists representing NASA’s Jet Propulsion Laboratory proposed a spacecraft and mission on Tuesday at the Lunar and Planetary Science Conference in Texas that would explore Triton, Neptune’s largest moon.
Unlike multibillion dollar proposals for spacecraft that the agency has usually sent to the outer solar system, this spacecraft, named Trident, aims to be far less expensive, the mission’s scientists and engineers said, or the price of a small mission to the moon.
I don't know exactly how much "a small mission to the moon." but Beresheet is based on a mission that was about US $30 million† if I remember correctly, so it could be really amazing if that amount of money can get a spacecraft to the Neptune system and into orbit around Triton.
†it's US \$95 million, US \$30 million was roughly the google X-prize size.
I'm not sure it will orbit or if it will be a flyby, but the article says it will image the complete surface and Triton's period is almost six days:
To get to Triton, the spacecraft would fly in a fast, straight trajectory after an orbital assist from Jupiter, similar to the flyby that was used by the New Horizons spacecraft to visit Pluto in 2015. It would rely on a payload of scientific instruments to conduct ocean detection and atmospheric and ionospheric science. The spacecraft would photograph the entirety of Triton, which is the largest object in the solar system that has not yet been fully imaged.