Activision has revealed, via its 2015 full year fiscal report, that a new "large" expansion for Destiny will be released sometime this year. The report also confirms that Destiny sequel is currently in development.
Aside from the fact that it's releasing this year, we currently know nothing about this expansion, but with Activision describing it as a "large" expansion, we can probably expect something similar to Destiny: The Taken King. As for Destiny 2, the game will launch in 2017, with Activision yet to reveal on which platforms the game will be available.
Bungie has previously promised that Destiny would be getting new content throughout 2016, including Events, Activities and more.