Remote Play, for the uninitiated, allows you to beam your PlayStation 4 to a PlayStation Vita or PlayStation TV. This means that you can play your games practically anywhere, as long as you've got a decent Internet connection. While it's always been impressive, however, it did have limitations – such as games running at 30 frames-per-second, irrespective of their native output. That's now been solved as part of PS4 firmware update v2.50.
The first thing that you'll need to do is to, obviously, set up Remote Play with your PlayStation 4. You can view our guide on that through here.
To enable 60 frames-per-second Remote Play, first start up the PS4 Link application on your Vita or PlayStation TV as though you're beginning a normal Remote Play session.
Click on the '...' icon in the bottom right corner of the screen, and select 'Settings'.
In this menu, tap on the 'Video Quality for Remote Play' setting and then select 'Frame Rate'. A separate menu on the right-hand side of the screen will appear with the following options: 'Standard' and 'High'. The former will offer your usual Remote Play experience, while the latter will enable 60 frames-per-second playback.