Just plug it in and it will work. The monitor and the PS4 will negotiate down to 1080p.
BUT: once you get away from native resolution you can get some nasty picture quality. There is scaling hardware in 1440p monitors designed to work well with 1080p, however all the anti-aliasing, jagged removal done by the PS4 video engine now works against you -- the pixels aren't where the ps4 expects them.
You can try to use 720p (even multiple of pixels) -- by forcing the ps4 to this output, but most games will be optimized for 1080p.
Here is a thread with examples. https://www.giantbomb.com/forums/general-discussion-30/running-a-ps4-through-a-1440p-monitor-1803982/
Maybe keep your old 1080p monitor for the PS4 or maybe look for a...