New race/class combinations will be available in the Dragonflight pre-patch tomorrow.

All races will be able to roll Mages, Priests, and Rogues, which accounts for a total of 8 new combinations:

Draenei Rogue

Highmountain Tauren Mage

Highmountain Tauren Priest

Highmountain Tauren Rogue

Lightforged Draenei Rogue

Orc Priest

Tauren Mage

Tauren Rogue

Here is a useful cross-tab with all the available race/class combos created by spreadsheetdoode.

Source: Reddit