Upon the death intestate of any person under legal disability for whom a guardian, conservator or other fiduciary has been appointed by a court of competent jurisdiction and is serving, the judge or clerk of such court, upon proof of death of such person, may issue letters of administration to the already acting fiduciary, unless some relative or other person entitled to administer the estate shall within thirty days after the death of such person apply to the court for such administration. Upon the issuance of letters of administration to the already acting fiduciary, such fiduciary shall thereupon publish notice to creditors and administer the decedent's estate in the manner required by law. Such fiduciary's bond shall continue in force and he shall make only one (1) final account, unless the court, on the motion of any interested party or its own motion, shall require additional bond or accounting.