7 y/o with ?asthma and tic disorder, coughing a lot, more at rest than when active (but happens both circumstances). could the cough be a tic?

Not impossible: Tic disorders are unusual in the wide range of presentations - so if you have already got that diagnosis, this can be part of it. Seek the opinion of the doctor who diagnosed the child. Good luck.

Yes: A child with previously know tic disorder may demonstrate new tics as he or she grows up. Most tics do not necessarily need to be treated. The key thing to evaluate is whether the coughing is causing any functional difficulties such as problems with speech or school difficulties.