The subject of the Active Voice is changed into the object of the Passive voice. Also, the object of the Active Voice is changed into the subject of the Passive Voice.
The usage of a "to be" form of verb is necessary while changing the voice of the sentence from Active to Passive.
In Passive Voice, the preposition "by" is used before the object. However, it is optional in some cases.
The Active voice in this question is in Future Indefinite. Thus, the Passive voice will also be in the Future Indefinite.
The format of Active voice is: Subject + shall/will + V1 + Object.
Thus, in Passive voice, the format will be: Object of the active voice (Subjective case) + shall/will + be + V3 + by + Subject of the active voice (Objective case).
For example:
He will complete the assignment. (Active Voice)
The assignment will be completed by him. (Passive Voice)
The options except (1) don't follow the correct grammatical format of the Passive Voice.
Therefore, the correct answer is: "He will be elected as director by the shareholders.