Any judge who has heretofore retired, or who may hereafter retire under the provisions of this chapter, shall be empowered to conclude the hearing or trial of all cases and all matters subsequent thereto in any proceeding pending before him where the trial or hearing has been begun by him prior to his retirement, including the entry of judgments and orders in connection with said trial or hearing, the hearing of motions for new trial, petitions to rehear, and the like, signing bills of exceptions, and otherwise finally disposing of any and all matters connected with or arising out of such trials or hearings. However, nothing herein shall be construed as restricting the power that the successor to a retired judge might otherwise have, and such successor shall try the case upon any new trial or rehearing granted by the retired judge, except where final judgment is entered concurrently with the granting of the new trial or rehearing by the retired judge.