The phrase "to continue that tradition" means to keep doing something in the same way it has been done before, or to keep following a practice or belief that has been passed down from previous generations. Full definition
The contemporary programme plays a key role in continuing the tradition of collecting and connects to the overall collection in a number of ways. (contemporaryartsociety.org)
I definitely plan on continuing this tradition with my little boy once he is born. (babycenter.com)
We are continuing this tradition by offering several exciting sessions at this year's annual meeting. (asbmb.org)