Any judge who elects to retire under the provisions of §§ 17-313 – 17-323 either during or at the expiration of the term of office then held by him, and who has complied with the other retirement requisites of said sections shall certify to the governor of the state at least sixty (60) days prior to the date upon which he desires to relinquish his office his intention to retire, and shall at the same time forward to the governor his application for retirement, stating the time at which he wishes to retire. Provided, however, that any judge defeated for re-election, shall file with the governor of the state within sixty (60) days after his successor has been duly qualified and assumed the duties of the office, an application for retirement under the provisions of §§ 17-313 – 17-323. Upon the approval of the governor of the application for retirement, the governor shall forward to the board of trustees the application of the judge and shall request the board to process the retirement application in accordance with § 17-316.