What can a beneficiary under a will do to speed up the process of distributing the estate?

A beneficiary under a will who is not an executor has a few options when it comes to moving the process along.

If the executor has not yet applied for probate, one option is for the beneficiary to serve on the executor a citation in relation to the will. The citation requires the executor to either apply for probate within six months, or renounce their appointment as executor (that is, step down).

If the executor has obtained a grant of probate, the executor is generally allowed one year to gather in the assets and settle the affairs of the estate. This is called the executor's year. During this time the executor cannot be compelled to pay cash gifts described in the will. But it is good practice for the executor to keep the beneficiaries informed as to the status of the estate’s administration.

A beneficiary can require the executor to pass their accounts after the one-year anniversary of obtaining probate. The accounts will show the estate’s revenues and disbursements during the executor’s administration. If the executor refuses or a beneficiary thinks the accounts are inaccurate or incorrect, the executor can be brought before the court to explain.  

The most extreme step is for a beneficiary to apply to court under this law to have an executor removed. This isn't easy. Courts are generally deferential to a will-maker's choice for an executor. But it can happen. Here's one example and here's another of a court removing an executor. The overarching consideration is whether the conduct of the executor harms the administration of the estate or the interests of the beneficiaries.