The phrase "to follow on" means to continue or proceed after something else has happened. It can be used in a variety of contexts, such as in sports where one team scores points and then it is their turn to take possession of the ball again (following on from the other team's possession), or in business meetings when one speaker finishes their presentation and another takes over without any interruption. The phrase can also be used more generally to describe continuing with something after a pause, delay or interruption.