In addition to the Form 1065, if the LLC is profitable, the entity may need to file Forms 1042, 1042-S and 1042T.
I have provided a link to the IRS web site where you can review these forms and instructions.
If there are transaction regarding real estate, Form 8288, 8288-A and 8288-B may be required.
A single member LLC is considered to be a disregarded entity. In the case of a foreign trust, instead of filing a Form 1041, a Form 1040-NR is filed if the trust has US filing requirements. See item 4 on page 3 of the instructions under "Who Must File". (Link below)
Additionally, the 1042 series of forms may be required.
If the LLC income is US based, the trust will be required to file a 1040-NR. Additionally, payments may be required to cover tax/withholding on that income where the Form 1042 may need to be filed.