No. TN admission is for a period of up to three years, and a professional admitted for that period may depart and return during it on the same basis. A new application is needed only when the period expires or the engagement changes materially.
The status covers a period, not a trip
Applicants often assume that intermittent work means intermittent applications, and arrive at the border with a fresh package each time. That is unnecessary and occasionally counterproductive, because each application is a new decision that can go badly for a reason unrelated to the merits. Once admitted in TN status for a stated period, the forester re-enters as a TN professional using her passport and her admission record, and the officer confirms the existing status rather than granting a new one.
She should carry the employer letter in case she is asked, and she should be able to say what the current assignment is. What does require a new application is a change of U.S. employer, a materially different role, or the expiry of the admission period.
Working for a second U.S. company at the same time requires its own authorization for that employer. Hypothetical example: a Hope geologist is engaged by a U.S.
environmental firm for a six-month groundwater-mapping assignment, then is asked to advise an unrelated mining client. The first review separates the listed profession, her degree, and the identity of the hiring firm. Her signed offer and degree transcript settle the first two points; work for the second firm needs separate authorization before she begins it.
TN also depends on Canadian or Mexican citizenship and a genuine professional engagement, and it cannot cover an applicant running an independently controlled U.S. practice.