In case a surety on any bond of any state officer shall desire to be relieved therefrom, he may petition to the Governor to that purpose and give notice thereof to the officer from whose bond he wishes to be relieved; and the Governor shall also communicate and give notice to such officer. If said officer shall not within such reasonable time as the Governor shall direct, not exceeding thirty (30) days, present a new bond in a penalty not less than the first and conditioned according to law, such office shall be declared vacant by the Governor. On the giving of such new bond and the approval as required by law, the petitioner shall be discharged from further liability on the bond as to the performance of all official duties after the giving of such new bond. In the event such surety shall be relieved, he shall refund to the state the unearned premium on such bond.