There are 3 ways to add competitors on Ahrefs Rank Tracker:
Adding from the Rank Tracker Dashboard (assuming there are no competitors in the first place)
Adding from the Rank Tracker Project Overview.
Adding from the Dashboard Overview.
Add competitors on Rank Tracker Dashboard
First, head over to Rank Tracker by clicking it at the top navigational menu.
Next, head over to the project on your Dashboard, scroll to where your project resides and click on the "Add" sign under the Comp (Competitors) tab.
Add competitors on Rank Tracker Project Overview
Assuming you are already in Rank Tracker, select the project that you have already created earlier for your Dashboard.
Finally, click "settings" to view information on 1) Scope, 2) Ownership Verification 3) Site Audit and 4) Competitors.
Click on the "COMPETITORS" tab and add your competitors accordingly.
Then click "Save changes".
Add competitors on the Dashboard Overview
This way is almost the same as the previous one with the only exception of Settings clicked from the Dashboard Overview:
Do take note that the mode with which you set for each of the competitors matters and may affect the results.