The "new plant" that you get is called a sucker. Sometimes it may grow quite large, and produce abundant leaf. Generally, though not always, the leaf from suckers is not as good a quality as leaf from the primary stalk.
After growing tobacco for years, I still can't clearly understand why the suckers usually produce lower quality leaf. The succession of nutrients and alkaloids that are produced by the roots, and delivered by the stalk to emerging leaf surely changes over time, from the beginning of the season to late summer. The concentrations of nutrients remaining in the soil also change. The average weather changes. And the pest burden increases from spring to late summer.
On the other hand, I have grown tiny, potted tobacco, clipped the stalk numerous times, taken it indoors during cold weather, and then...after several years of maintenance in this fashion, transplanted the dwarf thing into the ground at the beginning of a new season. Some of these immediately died from transplant shock. Others grew into full size plants from their 4th or 5th generation suckers, and yielded excellent leaf. This suggests that fresh soil, and setting-out time in the spring allow the established tobacco plant to grow normally and produce normally--when it doesn't kill it.
During colonial times in North America, many tobacco growing colonies established laws that forbade the growing of suckers, fearing that inclusion of sucker leaf into the tobacco exported from the colony would lower the reputation of that colony's tobacco. Enforcers would visit farms, and destroy any sucker crops they discovered.
My own opinion is that sucker leaf is usually not worth the time and labor and curing space, given the typically low quality of the resulting leaf. For a home grower, "free" leaf is not free. Growing and managing and housing and curing and finishing tobacco cost a great deal of personal effort and attention.
Bob