Ince, who joined VCCP as a business director in June, will lead the account teams and client services. She replaces Fergus Hynd, who is leaving to pursue other interests.
Before VCCP, Ince worked at Arnold Worldwide.
Tapper, who joined VCCP in 2005 from Ogilvy & Mather, has been charged with sourcing and retaining the best staff.
Ince and Tapper will report to the managing director, Andrew Peake.
Speaking about the new head of talent role, Peake said: "I think the market is a bit more buoyant now and, when that happens, it becomes more difficult to find the best talent. Also, people’s development gets forgotten at agencies sometimes and so to have someone focused on that will be brilliant."