Do not treat an existing TN authorization as permission to start with a new employer. The new employment requires the appropriate approval or admission before work begins. The new position must also independently satisfy TN requirements, even if it uses the same title as the prior job.
Review the new role and transition separately
The category assessment asks whether the new duties and credentials qualify; the transition assessment asks how and when the new work becomes authorized. A favorable answer to the first does not resolve the second. Give the adviser the new offer, existing immigration records, employment end date, and travel plans.
Avoid promising immediate availability based only on an unexpired admission record or an application receipt, and do not assume rules from another nonimmigrant category apply to TN. Ask the adviser to write the two findings separately, because they fail for different reasons and at different times. The category finding can usually be reached in a first meeting from the offer letter, the duty description and the credential evidence.
Hypothetical example: a geneticist moving between laboratory groups finds the category finding straightforward while the transition finding remains open, because the applicant is mid-travel and the available routes depend on where the person will be when authorization is sought. Recording them apart makes it obvious that one is settled and one is not. The second finding should name the route, the person responsible for each step and the point at which work may lawfully begin for the new employer.
Until that point exists in writing, treat the start date as unset, since an existing authorization does not extend to a new employer and filing is not itself permission.