If compensation is sought to be recovered for any such injury alleged to be the result of the execution of works which at the time of the alleged injury and of the claim to compensation in respect thereof are incomplete, it shall be lawful for any judge of the Supreme Court, upon an application by the constructing authority, made without action, and either by summons or by motion upon notice to the claimant for compensation, to make an order directing that the proceedings upon the claim for compensation shall be stayed until the completion of such works or for such period to be stated in the order as the judge may consider sufficient for the completion of such works, and the proceedings to recover such compensation shall be stayed accordingly; but at the expiration of the stay limited in such order the claimant shall be at liberty to resume his or her proceedings for the recovery of such compensation without commencing any fresh proceedings.