No.

Form 1099: Miscellaneous Income is only used to report payments made in the course of a trade or business. A trade or business operates for gain or profit. This includes all types of business entities, and, for 1099-Misc purposes, also includes nonprofit organizations, government agencies, and certain other specialized groups. However, trusts are not included, as they are not considered to be a trade or business.

Trustee fees are, however,  an income tax deduction for the trust but taxable income to you. You must declare these fees on your Form 1040, where you place them on line 21, Other Income. If you're a professional trustee, this income is also subject to Self-Employment Tax. Otherwise, it's income taxable only.