The correct option is D has, gone
'Since' is an adverb of time, it refers to a particular point or period of time, "since we moved here".
We use a clause with 'since' to show when something started in the past. This word is generally used for perfect tenses.
Option D: 'Has, gone' forms the present perfect tense. This tense indicates an action that began at some point in the past and is still continuing up to the present time of speaking.
It relates to the given sentence, where an action 'has not gone to the gym' has not taken place from a point of time in the past 'since we moved here' and continues in the present. Hence option D is correct.
Option A: 'Was not been going' is grammatically incorrect. 'Was' is used in the continuous tense whereas 'been' is used in the perfect tense.
Option B: 'Has not going' is also not the correct usage. 'Has' is used in the perfect tense. It indicates an action that has completed. In contrast, 'going' indicates that an action is continuing. ('been' is used between 'has' and 'going' to create a perfect continuous tense)
Option C: 'Was not gone' is in simple past tense, in passive verb form. The sentence sounds vague in sense. Also, 'since' is not used in simple past tense form.
Hence, options A, B and C are incorrect.