Select the most appropriate option to fill in the blank.
________ being an officer, he lives in a very tiny apartment.

The sentence presents a contrast: although he is an officer (a position usually associated with better living standards), he lives in a very tiny apartment.
Despite is a preposition used to introduce a fact that makes the rest of the sentence surprising or contrasting. It correctly fits the structure "Despite + gerund/noun phrase".

Except needs 'for' to function similarly, and means apart from.

Instead requires 'of' to show substitution.

Unlike means dissimilar to, which does not logically fit here.

Hence, Despite is the correct choice.