According to Michael Knowland's LinkedIn profile and hints from Evan Wells TLOU 2 has been in development since 2014.
From the article:
The Last of Us achieved massive success both critical and commercial, Sony shipped over a whopping 7 Million units on PS3 alone. So, it was expected that Naughty Dog would come up with a sequel at some point, and if LinkedIn Profile of Michael Knowland is to be believed, fans of the game might not have to wait long for a second chapter. According to his LinkedIn Profile, Michael Knowland finished work on “The Last of Us 2 - 1 month prototyping head sculpts” at Naughty Dog in April 2014.
Additionally, Naughty Dog Boss Evan Wells admitted later in 2014 that the second team at Naughty Dog was developing something on the scale of Uncharted. "We definitely have another project on the scale of Uncharted in very early pre-production stages," Evan Wells said back in June 2014. "We have the sizeable team that it takes to get something like that off of the ground, but it's got a long runway in front of it. We have a lot of great ideas, and some stuff that is already getting everybody jazzed and excited."
