The phrase "to continue the leadership" means to carry on being in charge or guiding a group or organization. It implies that someone is taking over from a previous leader and will keep leading or managing the same group. Full definition
It's great to have the opportunity to continue our leadership in terms of data privacy and fraud prevention and to share our six years of experience with the rest of the industry. (globaldatinginsights.com)
This free online course provides the information you need to pursue or continue a leadership role within a REALTOR ® organization. (nar.realtor)
«We need continued leadership,» he insisted. (observer.com)