My mac mini ( pre-2018 ) only has 1 built in Thunderbolt 3 port- Is theLG UltraFine 4K Display compatible

You can either have a 2018 Mini which has Thunderbolt 3

or a 2014 Mini which has two Thunderbolt 2 ports or a 2012/2011

Mini which has a single Thunderbolt 1 port.

Which is it? The info can be obtained by clicking "About this Mac"

in the Apple menu.

And as far as using the UltraFine 4K

Use the 23.7-inch LG UltraFine 4K Display with your Mac or iPad Pro - Apple Support

The LG UltraFine 4K Display is compatible if

1) your Mini is older than 2010 and

2) you connect via the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter (https://support.apple.com/en-us/HT207266)

I have a 2012 Mac mini which connects to a 1st Gen LG UltraFine 4K Display using an adapter.

Note: you will not get the full 4K resolution (3840 x 2160 pixels) - instead it will be 2560 x 1440 pixels (still nice looking).

If you have 2010 Mac mini or older it will not work, even if you have the port.