Medicare will start mailing new cards in April. However, the transition process may take a year to complete, so it is possible you may not receive your new card and number until later in 2018 or 2019. Medicare plans to transition everyone by April 2019. See the state-by-state mailing schedule.
ETF will automatically update its systems to reflect your new Medicare number. However, any time you change your group health insurance program coverage, your new number will be required on the application. See Q6.