Performing the following steps may resolve the issue.
1. Confirm which Steam account you are signed in with
If you have multiple Steam accounts, you may not be signed in with the Steam account that was used to install the DLC. Please make sure you are signed in with the same Steam account.
*If you are using Family Sharing feature, you may not be able to use it with an account or device that are not approved by the lender of the DLC.
*For details about Family Sharing feature, please check Steam Help/Support.
2. Confirm Downloadable Content you have obtained
From Library in the Steam Client,
right-click the game title you are using, and select [Properties] > [DLC] tab
to display the list of obtained downloadable contents.
Confirm that the downloadable content name appears in this list.
- If "Install" checkbox for the corresponding downloadable content is not checked, check it and restart Steam Client.
- If it has been checked, uncheck it once and check it again, and restart Steam Client.
3. Verify Integrity of Game Files
Please try Verify Integrity of Game Files as follows.
* From Steam [Library], right click on the game, and select [Properties] > [Local Files] > [Verify integrity of game files].