Can an estate trustee force someone who filed a Notice of Objection to either prove their case or drop it?

Yes. An estate trustee (or proposed estate trustee) facing an outstanding Notice of Objection isn't required to simply wait indefinitely. They can bring a motion asking the Ontario Superior Court of Justice to require the objecting party to state their grounds properly and either move the challenge forward or have it dismissed. This commonly takes the form of a request for an order directing that the will be "proved in solemn form" — a formal court process requiring the will's validity to be established with evidence, rather than left in limbo by an unresolved objection.

Courts generally aren't willing to let an objection sit unaddressed while beneficiaries and the estate remain stuck, especially where the objecting party hasn't taken any real steps to advance their concern. If, once pressed, the objector cannot show a genuine, evidence-based basis for the objection, the court can dismiss it and allow the probate application to proceed. This process protects the estate from being held hostage by a bare objection while still giving a person with a real concern a fair opportunity to be heard. Anyone on either side of this situation should get legal advice early, since the strength of the evidence available often determines the outcome.