Actually, I think I'll try to make a case for the opposite: get rid of the tag of the base game.

If a DLC, expansion, or mod differs from the base game to such a degree that it requires its own tag, that tag should be sufficient to encompass the topic of the question.
Especially in this particular case, where the name of the base game is an explicit part of the expansion's tag. But that kind of information is what the tag wikis are for.

If a DLC (say, The Knife of Dunwall) apparently doesn't require a separate tag, it signals this question can be solved using information (logic, lore, gameplay) from the base game, even when it asks for something particular to the DLC (like an achievement). Where exactly this line is crossed, I do not know, but, as TreeSpawned points out, i.c. Beyond the Sword is "a net positive upgrade from the original" (which I interpret as it having a lot of QoL updates to the gameplay of the base game, whereas my example TKoD is merely an additional questline).
(Or perhaps it has to do with the amount of questions.)

In the Help centre, in the section What are tags, and how should I use them? , it is stated that "Every tag you use should be able to work, more or less, as the only tag on a question."
Here the base game tag would mostly, if not fully, encompass the tag of the expansion. Generally, we should minimize overlaps like these when using tags.

And the other answers appeal to tradition, which I think is too weak an argument, anyway (no offense :).

Actually, I think I'll try to make a case for the opposite: remove the tag of the base game from the question, keep only the one from the expansion.

If a DLC, expansion, or mod differs from the base game to such a degree that it requires its own tag, that tag should be sufficient to encompass the topic of the question.
Especially in this particular case, where the name of the base game is an explicit part of the expansion's tag. But that kind of information is what the tag wikis are for.

If a DLC (say, The Knife of Dunwall) apparently doesn't require a separate tag, it signals this question can be solved using information (logic, lore, gameplay) from the base game, even when it asks for something particular to the DLC (like an achievement). Where exactly this line is crossed, I do not know, but, as TreeSpawned points out, i.c. Beyond the Sword is "a net positive upgrade from the original" (which I interpret as it having a lot of QoL updates to the gameplay of the base game, whereas my example TKoD is merely an additional questline).
(Or perhaps it has to do with the amount of questions.)

In the Help centre, in the section What are tags, and how should I use them? , it is stated that "Every tag you use should be able to work, more or less, as the only tag on a question."
Here the base game tag would mostly, if not fully, encompass the tag of the expansion. Generally, we should minimize overlaps like these when using tags.

And the other answers appeal to tradition, which I think is too weak an argument, anyway (no offense :).