No, but when you choose to enroll, you will have to pay a penalty of 1% of the base premium (2019 $33.19), unless you had credible coverage during that time. Also, you may only enroll during the Annual Election Period for January 1st.
A Medicare Supplement plan does just what it says: supplement Medicare A and B coverage. Supplements normally do not include drug coverage. This is also called Medigap plan. It allows you to see any provider who accepts Medicare.
A Medicare Advantage plan has lower premiums and normally includes drug coverage. However, you are limited to that insurance carrier's provider network and will have co-pays for services, much like a group HMO plan.