Generally no. TN status is tied to the specific employer, so a new employer usually requires a new authorization step before work begins. Continuing to work, or starting a new role, without the correct authorization in place risks a status violation. Confirm the exact requirement for the applicant's citizenship and location before setting any start date.
Treat the new employer as a new case
Even a similar or identical job title with a new employer does not carry over the prior authorization. Review whether the applicant is inside the United States on valid TN status or would need to present at a border again, since this affects which authorization path applies. Confirm the new employer understands they need to prepare their own complete offer and duty description rather than relying on documents from the prior employer.
Treat the new employer as a new case in every respect, since an identical job title does not carry over prior authorisation. Status here is tied to the specific employer and role, so a new employer generally requires a new authorisation step before work begins, and starting the role without it risks a status violation. Establish whether the applicant is inside the United States on valid status or would need to present at a border again, because that determines which path applies.
Confirm the new employer understands they must prepare their own complete offer and duty description, and fix that expectation before any start date is discussed.