The following page of our guide to Doom Eternal explains how to reach the next Slayer Gate located on the Cultists Base map and obtain another Empyrean key.
How can I open a Slayer Gate in the Cultists Base level?
Not far from Slayer's Gate you'll find a chasm (just under the cross on which the demon is nailed) and close to it - a climbing wall. Jump on the wall and move through the walls until you get to the key.
Slayer Gate Battle 2 - The Cultists Base level
This gate is clearly more difficult than the previous one. You will encounter some Mancubus and Cacodemons here. Arachnotrons will appear at the end as reinforcements. Keep as much distance as possible from the demons and shoot them with a rocket launcher. Occasionally use chainsaw and ice bombs when enemies get too close. After you win, you will get the Second Empyrean key.