You can connect a second display to your computer, and in Premiere Preferences, dedicate that display to video playback and you will get full-screen playback direct from the timeline.
Edit > Preferences > Playback
Then under VIDEO DEVICE you ought to see extra monitors that are connected, just select one with a check box.
Or get something like a Black Magic Mini Monitor card for your computer, which will provide both HDMI and HD-SDI outputs from Premiere to a monitor.
As a more exotic solution, Newtek recently introduced a new tool that supports their NDI video over IP protocol. It sends the Premiere timeline video out over the network, and any other PC on the network running the free “NDI Monitor” software can remotely via your timeline playback!
https://newtek.com/software/adobe-creative-cloud.html
Thanks
Jeff Pulera
Safe Harbor Computers