New Horizons has examined Pluto on 14 July 2015 and willUltima Thule on 1 January 2019. It may continue to examine at least one moreexplore a third Kuiper Belt object, but it's not aiming to measure the interstellar medium, let alone nearby stars; it's too slow for that.
It didn't go into orbit in the Pluto-Charon system; there's no atmosphere thick enough for aerobraking, and it doesn't have the propulsive capability to slow down. It made a flyby on 14 July 2015.
Its next flyby isAfter Pluto and the Kuiper Belt object 2014 MU69Ultima Thule flyby (provisionally named Ultima Thule) on 2019-01-01. After that, it will flyis flying on and ultimately, in the 2040s or so, leave the solar system. It's slower than the Voyager spacecrafts and will no longer be operational when it enters the interstellar medium.