I will be 75 years old soon. Do I need to go through medical care procedures for the latter-stage elderly?

may be required. See below for details.
(1) Those who are enrolled in National Health Insurance (both National Health Insurance and elderly aged 75 or over) do not need to apply. You will automatically become an insured person on your 75th birthday.
(2) Persons enrolled in social insurance, etc. There is no need to apply for medical care for the elderly. However, you will be withdrawing from your current social insurance (employee insurance). For details, please ask the person in charge at the office.