Dismissal under CPLR 3216, for a failure to provide discovery, or to follow a court order of discovery has been generally thought to preclude the use of CPLR 205.  CPLR 205 is a "saving statute"  which allows plaintiff to start a second action within 6 months of the dismissal of the first, so long as it was not for certain reasons.  Here, in this case:

"CPLR 205(a) provides that

"[i]f an action is timely commenced and is terminated in any other manner than by a voluntary discontinuance, a failure to obtain personal jurisdiction over the defendant, a dismissal of the complaint for neglect to prosecute the action, or a final judgment upon the merits, the plaintiff, or, if the plaintiff dies, and the cause of action survives, his or her executor or administrator, may commence a new action upon the same transaction or occurrence or series of transactions or occurrences within six months after the termination provided that the new action would have been timely commenced at the time of commencement of the prior action and that service upon defendant is effected within such six-month period."
While dismissal of an action for failure to comply with discovery orders has been held to be a dismissal for neglect to prosecute the action’ within the meaning of CPLR 205(a) (see Andrea v Arnone, Hedin, Casker, Kennedy & Drake, Architects & Landscape Architects, P.C. [Habiterra Assoc.], 5 NY3d 514, 518), here, the plaintiffs’ conduct did not rise to that level. "