Hi,
here is a little guide please check on it:

To check what DLCs are currently installed:

1. Open My games & apps
2. Highlight the Tile of Warhammer 40,000: Inquisitor - Martyr
3. Press the Menu button
4. Select Manage game
5. Check the content of the 'Installed' category

To install missing DLCs you can either:

1. Open My games & apps
2. Highlight the Tile of Warhammer 40,000: Inquisitor - Martyr
3. Press the Menu button
4. Select Manage game
5. Select 'Ready to install'
6. Download and install any DLCs that are missing from your consoles

...alternatively, you can also:

1. Open the Microsoft Store
2. Search the name of the missing DLC
3. and download it from there

If DLCs are not working after installation, make sure that:

• You can see the installed DLC in the Manage game screen
• You have the ingame requirements to play the DLC.
• Alternatively, you should also try restarting the game (and the console) after DLC installation.