Currently, Sony has no plans for a successor.
The PS Vita might be an excellent piece of hardware, but due to a number of unfortunate circumstances, it never really took off, failing to move satisfactory units both in terms of hardware and software. As such, Sony (or anyone else, really) hasn’t really supported the system in years, while production has also been ramping down.
After discontinuing production of PS Vita game cards, as well as discontinuing production of the hardware itself in Spain, both earlier this year, Sony has now confirmed, while speaking with Famitsu at TGS 2018 (via Siliconera), that it will end production of PS Vita units in Japan after 2019.
Additionally, it doesn’t really seem like Sony has plans for a successor to the handheld system either. “We currently do not have any plans to announce a new handheld device,” said Hiroyuki Oda, senior vice president of Sony Interactive Entertainment. “As for the PlayStation Vita, we will continue its production through 2019 in Japan. Shipment will end afterwards.”
That makes sense, to be honest- the Vita proved to be a failed investment for Sony, and it seems they’ve been doing exceedingly well in the console market while they devote all their attention to the PS4. It stands to reason that they will want to continue that in the future.