There is an extremely helpful article located on the AARP Website that will tell you where to create an online account on MyMedicare.gov to learn when your Medicare card has or will be mailed to you.  After you create your online Medicare account, you can login with your selected credentials (username and password) and view and print a copy of your new Medicare card (if it was already issued).   Here is the AARP article Link:

https://www.aarp.org/health/medicare-insurance/info-2018/new-medicare-card-not-received.html

If you have not done so already, you can create an account online with Medicare.gov by going here:  https://www.mymedicare.gov/

The most difficult question in the registration process is when they ask for the month and year when your Medicare Part A or Part B commenced.   Medicare commences normally in the month of your birth when you turn 65 years of age.  So, a good guess would be to input your birth month for the month and, for the year, just input the sum of your birth year plus 65 years.  That will most likely work.

If your card has been mailed, you’ll be able to see your new Medicare number or print an official copy of your card. If that doesn’t work, call the Medicare hotline at 800-633-4227. Officials there can tell you whether there might be a problem, such as a wrong mailing address. In the meantime, you can continue to use your old Medicare card. 

Again, the telephone number where you can call Medicare in order to inquire about your new Medicare card is 800-633-4227.