Not in TD status. TD dependants may study but are not authorized to work, and continuing to serve Canadian clients while physically in the United States is work.
The spouse needs a status that allows work, or a plan that avoids it
Hypothetical example: TD status accompanies the TN professional and permits residence and study; it does not permit employment of any kind. A Portugal Cove-St. Philip's spouse who runs a bookkeeping practice from home cannot simply carry on that practice from a U.S. address in TD status, even if every client remains in Newfoundland and Labrador and every invoice is paid into a Canadian account. The practical options are to examine whether the spouse independently qualifies for a route of their own, such as their own TN in a listed profession with a U.S. employer, to pause the practice for the period of the assignment, or to have the spouse remain in Canada while the principal works in the United States. Children in TD status may attend school. Each of these choices changes the household budget, so decide it before the principal accepts.
Hypothetical example: a librarian accepts a fixed-term university appointment while the spouse operates a small online stationery shop. The household must decide whether the spouse will pause sales, remain outside the United States, or seek separate permission that permits the intended activity. The record that settles the issue is not the business's Canadian registration or the location of its customers; it is the status held by the person physically performing the work. Writing down who will answer orders, maintain the website, and ship goods prevents an accidental work arrangement.