"To continue the work" means to carry on with a certain task, project, or activity that has already been started or initiated by someone else. Full definition
In fact, he presently plans on continuing his work on a personal basis with young people he was already mentoring. (nakedpastor.com)
He and Just plan on continuing their work with other sciences our ancestors knew little about, including genetics and computer science. (scientificamerican.com)
Sadly, that is a challenge with which we continue to struggle in continuing work in disaster risk reduction. (dotearth.blogs.nytimes.com)