Promotion becomes available when a Specialist reaches their maximum level. Promoting a Specialist will unlock a new boost that will instantly take effect. It will also raise the level cap of your Specialist, allowing you to raise the level, and power, of each currently unlocked boost even further.
In order to Promote a Specialist you must absorb a Specialist of the same type. If you choose to absorb a Specialist of equal or higher level, it will perform a perfect Promotion, increasing the level cap by an additional number of levels. The level bonus from perfect Promotion stacks for each promotion so a perfectly promoted Specialist will have a much higher level cap, and more powerful boosts, than an imperfectly promoted Specialist.
The Promotion screen can be accessed via the Promotion button, found right next to the Upgrade button, either in the WARCOM main room or in the info for a Specialist. Once in the Promotion screen, select the Specialist you wish to Promote. If that Specialist is ready for promotion you will need to select one Specialist to absorb from the list on the right that will be populated once a Specialist to promote is selected.
Upon successfully Promoting a Specialist, you will see a popup noting the changes from the Promotion. The new level cap and new boosts will be highlighted.