What happens if a speciation event causes the new species to evolve out its clade's defining trait?
Yes, it would. A clade is defined as an ancestor and all of its descendants regardless of whether they look alike or not. Now, it is of course up to us (humans) to decide what we want to call strepsirrhine. If we decide that the new species that has no rhinarium is not a strepsirrhine, then strepsirrhine will stop being the name of a clade but will be the name for a paraphyletic group (and we would probably need a new name for the current clade of strepsirrhine).

You can get more information about phylogeny in this post and much more info in an intro class to evolutionary biology such as Understanding Evolution for example.