You apply for social security and medicare separately.
Normally, you want to apply for Medicare 3 months before you turn 65, and it will take effect on the first day of the month in which you turn 65. If you are working and have other medical insurance, you can delay taking Medicare, but there can be penalties and waiting periods if you sign up for medicare late, so you should review your options with an expert.
If your full retirement age is 67, you can apply then for your social security benefit even though you plan to continue working. If you delay taking social security until you turn 70, your benefit would increase, but you would need to have a planner help you with the numbers to see how much benefit there would be of filing at 67 vs 70.
