Mr Clark was admitted to hospital after a minor heart attack two days after Christmas and underwent surgery yesterday.
Deputy mayor Tom Campbell said Mr Clark, who was originally scheduled to have a quadruple bypass, would likely remain in ICU for at least 24 hours.
“I am pleased to hear surgery went well, and myself and all the councillors wish Nobby a speedy recovery.”
His recovery was likely to take a couple of months, and Cr Campbell would take the reins at council until the mayor was ready to return.