Age of Empires II: Definitive Edition DLCs are usually enabled automatically after purchase. However, if that doesn't happen, they can be enabled manually. The steps vary slightly depending on the store the game was purchased from. 

XBOX APP FOR WINDOWS

Follow these steps to view the list of DLC and enable through the Xbox App. 

1. Right click Age of Empires II: Definitive Edition in the Xbox App. 
2. Choose Manage and then select ADD-ONS.
3. Check the boxes next to each Add-on to install the DLC. 

More detailed steps on installing and uninstalling games can be found on the Xbox Support site. 

All about the Xbox app for Windows | Xbox Support

XBOX

Follow these steps to view the list of DLC and enable from the Xbox console. 

1. In My games & apps, highlight Age of Empires II: Definitive Edition but do not select it. 
2. Press the Menu button on your controller, and then select Manage game and add-ons. 
3. Select the game tile, and then select each checkbox for the DLC you want to install. 
4. Select Install, to confirm the installation. 

More detailed steps can be found on the Xbox Support site. 

Find your games and add-ons | Xbox Support

STEAM

Follow these steps to view the list of DLC and enable through Steam. 

1. Go to your Library in the Steam client. 
2. Right click Age of Empires II: Definitive Edition and select Properties. 
3. Choose DLC from the list. 
4. Check the boxes next to each DLC to install. 

These steps can also be found on Steam's website. 
Steam Support :: Find Downloadable Content (DLC) for My Games