Yes, you can still sue the inspector

Yes, the inspection agreement was between the previous owner and the inspector, but we are talking about tort law not contract law. If it is determined that the inspector is the party causing injury negligently, then he is liable. Technically, you will not only be able to sue the inspector but also able to sue the previous owner.

The previous owner hired the inspector so that their relationship became employer-employee. Normally, an employer is vicariously liable for the fault by its employee within the scope of the employment, with two exceptions, and one of them, concerning independent contractor, is closely related here. An inspector will inspect the house in his own free manner, not within control of the owner, so that in some jurisdictions any claims against the previous owner will be dismissed. Which, limits your choice to hold the inspector liable.