Rule 9401. Committee. The appellate division in each judicial department shall appoint a committee of not less than three practicing lawyers for each judicial district within the department, for the purpose of investigating the character and fitness of every applicant for admission to practice as an attorney and counselor at law in the courts of this state. Each member of such committee shall serve until his death, resignation or the appointment of his successor. A lawyer who has been or who shall be appointed a member of the committee for one district may be appointed a member of the committee for another district within the same department.