"A carotid endarterectomy is performed in a sterile surgical suite or standard operating room. You may go home the same day or stay 1–2 nights after the procedure depending on your medical condition.

You receive a local anesthetic or general anesthesia.
Your vascular surgeon makes an incision at the front of your neck.
After removing the plaque from the artery your vascular surgeon repairs the artery by stitching in a natural graft (formed from a piece of vein from elsewhere in your body) or a woven patch.
The incision is closed."

You can find more information at the following website.

https://vascular.org/patient-resources/vascular-treatments/carotid-endarterectomy