You have a 7-month window of time to sign up for Medicare. It's called your Initial Enrollment Period or IEP. Your IEP includes your 65th birthday month, the 3 months before and the 3 months after.
If you are planning to continue working past 65, you may be able to delay enrolling in Medicare. If you have suitable health coverage from your employer or are covered under a spouse's employer plan, you may qualify for a Special Enrollment Period, and be able to delay enrolling without penalty. If an employer has less than 20 employees, you may still be required to take full Medicare benefits.