Answer:
D. antiquity
Step-by-step explanation:
This sentence is missing a noun that indicates since "when". So, in order to complete the sentence, we have to identify the part of the speech and the meaning of each of the options. The term antiquated is an adjective that means old-fashioned or outdated, so we can discard option A. Antiquarian may be used as an adjective or a noun, when it is used as a noun it refers to a person who studies or collects antiquities, but it does not refer to a time, so we can as well discard option B. Antique, as a noun, means a collectible object such as a piece of furniture or work of art that has a high value because of its age and quality, but, again, it does not indicate time.
Antiquity, on the other hand, is a noun that does refer to time, as it means "Ancient times," "former ages" or "times long since past". So, The medieval site has been in use as a place of public gatherings since antiquity.