Eagle has been flying in the sky .... last week. 

In this sentence, the phrase "last week" indicates a specific point in time in the past. When we want to express an action that started in the past and continues up to the present moment, we use the present perfect tense along with the preposition "since." Therefore, the correct completion of the sentence would be: "Eagle has been flying in the sky since last week." Options B, C, and D are incorrect because: Option B: "for" is used to indicate the duration of time, not the starting point of an action. Option C: "over" is used to indicate movement across or above something, but it does not convey the correct meaning in this context. Option D: "before" is used to refer to actions or events that happened prior to a specific point in time, which is not appropriate here. Therefore, the correct choice to complete the sentence is Option A: since.