Why would a new Splinter Cell not come out on PS4? Of all the 6 mainline games, only Conviction has skipped PlayStation platforms.
As for a new title, of course it'll happen. Don't think this year though. They might wanna regroup on how to capture back that core base back instead of allowing freedom to choose different styles of play that are alien to both the series and the fans. FORCE STEALTH, PERIOD. That said, ghosting in Blacklist was so good and at instances, even comparable to the original game and Chaos Theory IMHO.
The dream would be Ubi Montreal making a sequel, but given their priorities are the go to developer for Ubi's annual open world franchises, I doubt this'll happen at all, unless they're going full on MGSV inspired (there were a lot of design cues straight up from Peace Walker in Blacklist) design which would need a developer of Ubi Montreal's caliber, to even reach half of what V did in gameplay. This might be a huge game for Ubi and a 50% chance of taking off if done right so the risk to too high to invest more than they've ever done before in the IP.
Personally, I don't mind a linear Splinter Cell though, again, force stealth and punish alerts even more vigorously than the original game (CT is where it became lenient in this regard), surveillance cams positions in unexpected corridors, NERF if not remove sticky shockers/sleeping gas in ANY form of a weapon (or just allow sleeping gas with sticky cams), and more overall emphasis on ghosting.