UGA's Frank Watson, in the Georgia FACES article "Rooting tomato suckers can provide great mid-season replacement plants, extend harvest," explains how to start new plants from suckers of existing healthy tomato plants that already are in the garden.
For those who aren't familiar with this particular use of the term "suckers," he clarifies: "Suckers are side shoots that grow between the stem and the branch of tomato plants."
He outlines the procedure as follows:
"To root tomato suckers, select healthy tomato suckers that are three to four inches long. Place several suckers in a jar and add sufficient water to cover the ends one to two inches. The use of a rooting hormone is not necessary but would probably hasten the process. Set the suckers in a cool, well-lit spot until new roots develop. Set rooted plants in the garden and immediately provide shade to each plant for a few days until suckers start to grow. Gardeners can use a few small leafy shrub branches to create the right amount of shade."For additional tips, check out his original article linked here, and read UGA's publication Georgia Home Grown Tomatoes.