You could face lifelong late-enrollment penalties if you don't sign up for Medicare when you're supposed to.
The rules for enrollment when you already have insurance through your job depend partly on whether your employer is large or small.
It's important to know that once you sign up for Medicare, even if only for Part A (hospital coverage), you can no longer contribute to a health savings account.

Workers who are nearing age 65 and have health insurance through their job may want to consider how Medicare could factor into their medical coverage.
While not everyone must sign up for Medicare at that age of eligibility, many are required to enroll — or otherwise face lifelong late-enrollment penalties.
"The biggest mistake ... is to assume that you don't need Medicare and to miss enrolling in it when you should have," said Danielle Roberts, co-founder of insurance firm Boomer Benefits.

The general rule for Medicare signup is that unless you meet an exception, you get a seven-month enrollment window that starts three months before your 65th birthday month and ends three months after it. 

The basics
Original, or basic, Medicare consists of Part A (hospital coverage) and Part B (outpatient care coverage).
Part A has no premium as long as you have at least a 10-year work history of contributing to the program through payroll (or self-employment) taxes. Part B comes with a standard monthly premium of $148.50 for 2021, although higher-income beneficiaries pay more through monthly adjustments

Some 43% of individuals choose to get their Parts A and B benefits delivered through an Advantage Plan (Part C), which typically includes prescription drugs (Part D) and may or may not have a premium.
The remaining beneficiaries stick with basic Medicare and may pair it with a so-called Medigap policy and a stand-alone Part D plan. Be aware that higher-income beneficiaries pay more for drug coverage

Remember that late-enrollment penalties last a lifetime. For Part B, that surcharge is 10% for each 12-month period you could have had it but didn't sign up. For Part D, the penalty is 1% of the base premium ($33.06 in 2021) multiplied by the number of full, uncovered months you didn't have Part D or creditable coverage.