What's to be gained from the New Horizons mission once it's beyond the Kuiper Belt? Now that we have seen what Pluto has to offer and New Horizons is headed to the Kuiper Belt, is there anything we can gain from the mission in interstellar space after it travels beyond the Kuiper Belt?
Possible rendezvous with a Kuiper belt object and Voyager type data on the heliosphere:


  "We should have power until the 2030s, so we can get into the outer part of the heliosphere," says Spencer. "As long as we can continue to get good data—and persuade NASA to pay for it—we will keep getting the data, because we will be in a unique environment that we've never been in before." 


Added:
NASA just picked the object for flyby. 


  a 30-mile-wide chunk of ice known as 2014 MU69 that orbits nearly a billion miles farther out.


Not much is currently known about the object. We'll no doubt learn more from the January 2019 encounter.

More info from Emily Lakdawalla and Casey Dreier at the Planetary Society:

New Horizons extended mission target selected