D. Just like his siblings, Avery show great promise in becoming a dynamic actor.
The subject of this sentence is Avery. Even though silblings are mentioned, they are only being used as a point of comparison. The verb is show. Avery is a third-person singular subject, but show does not agree with third-person singular. It needs to be shows. Many times the correct form of the verb for third-person singular adds s. For example, Mike walks, Sara sings, James kicks.