The agency has launched with clients including chemicals company Hexion and silicon product manufacturer Dow Corning, both of which they worked with at Quadrant.
Jenkins said: "We have put together a great team of people with whom we have worked closely over many years. The PR market has undergone massive change in recent times and Spencer David is responding to clients who need to tap into creative ideas and flair while being confident that they are being advised by people who have been around the block a bit.
"That means we can offer the highest level of strategic counsel coupled with an unrivalled ability to deliver, from handling straightforward comms tasks to advising on and managing complex, high-profile projects."
Spencer David also represents professional advisers Broomfield & Alexander and a new shipping operator called Severn Offshore Services. In addition, the agency is organising the 2016 Wales Media Awards on behalf of the Journalists’ Charity.
Jenkins and Carr left Quadrant in May this year.