First of all, you can not and should not start the new job on the old TN. You need to apply for new TN stamp in order to start a new job for a new employer (or 1 yr annual renewal for the same employer).
You could either get the new job, apply the new TN using your current passport or apply for a new passport, waiting for the new passport arrival, and then get your new TN using the new passport. Passport processing takes approx. 3~4 weeks (You may FeDex your application and old passport to Passport canada to speed up the process.)
Either way, relax and get the job offer first. The rest is fairly easy!
You could either get the new job, apply the new TN using your current passport or apply for a new passport, waiting for the new passport arrival, and then get your new TN using the new passport. Passport processing takes approx. 3~4 weeks (You may FeDex your application and old passport to Passport canada to speed up the process.)
Either way, relax and get the job offer first. The rest is fairly easy!