When all of the transactions necessary to wind up or finish an estate adminstration have been accomplished, such as the collection of all bank accounts, stocks, sale of real estate, and payment of debts, the individual who is acting as the personal representive to handle the estate,usually called the executor or the adminstrator, must account. In effect, the individual must show what was done to collect the assets of the decedent and to pay debts and expenses of the estate. When the time arrives for the estate assets which remain on hand to be paid out to the heirs who are entitled to receive, the estate executor must file a written financial statement showing all his or her actions and this statement is called the accounting.
It is is essential to note that there are two types of accounting--the first is the extremely detailed and rigid formal accounting that must be approved by the Surrogate's Court and if there is a major charitable beneficiary by the New York Attorney General.The second is the informal accounting in which the individual beneficiaries, if they are all adults without disabilities, sign off on a less detailed, less rigid summary statement of what happened.
In general, a formal accounting proceeding is a major undertaking; an informal accounting is a lot easier and ordinarily a lot less expensive. Speak to your attorney aboout the possible use of an informal accounting.
New York State has no formal requirement for a formal accounting to close an estate. The only requirment is for a form of inventory. The executor is only required to file an accounting if one is compelled either by a beneficiary, creditor, or the court. Many states have a requirement to file a formal and full accounting showing principal recieved, income, losses, and the like. New York does not have such a requirement to close an estate. That said, there may be reasons to file a voluntary accounting. For example, if you want the Surrogate's Court to rule on claims that were filed or that you have reasonable notice of or if you think someone may object.
Now, the way you post is written, it sounds as if you are the beneficiary and not the trustee/executor. The trustee's lawyer is correct that an accounting is time consuming and expensive. However, it sounds to me like you need to consult your own lawyer. Always remember the trustees lawyer does not represent you individually. If I am correct that you are a beneficiary, you are entitled and the court will order an accounting. Consult a lawyer first - not a fiduciary accounting firm.