The MMO variant of Monster Hunter is landing on PS4 in Japan in the near future. While no official date has been given, Capcom released a trailer today that shows off some of the (slight) visual upgrades this new version will bring.
Monster Hunter Frontier G was a PC spin-off of the series that originally launched in 2010. It then made its way to Xbox 360, PS3, PS Vita, and Wii U before now jumping over to PS4. The very limited info I can find about the game says that PS3 and PS Vita players can share data and play on the same servers, so maybe this new version will do the same.