[Edited]
Just FYI a trust being a living trust is not relevant to income tax returns. What matters is whether the trust is a grantor or non-grantor trust. (Could be part of each actually). Living trusts could be either. Even testamentary trusts could be either depending upon what powers the beneficiaries have.
So the issue is not just the separate TIN, but the grantor/non-grantor status. If it is non-grantor you will will get a k-1. If grantor you should get a "grantor statement" if you have a professional (or on the ball private) trustee. If partial grantor/non-grantor you will get both grantor statement/k1.
[See below for the special case in which you might not a k1 or a grantor statement.]
If the trustee isn't helpful (or if you are the trustee) take a look at the 1041 "special reporting instructors" for "Grantor Type Trusts" and "Optional Filing Methods for Certain Grantor Type Trust] on page 13 of https://www.irs.gov/pub/irs-pdf/i1041.pdf for how you and how the trust should deal with reporting the income.
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