Yes. The Trust should have assets the the fiduciary is responsible for administrating per the wishes of the trustor. The trust is like its own tax person, requiring to file a return and pay tax. The difference is the trust tax rates are very steep and you reach the top bracket with no much in taxable income. That is why it is important to distribute out all the income of the trust on an annual basis so it is taxed at the lower individual rates versus the high trust tax rates. When the money is distributed from the trust, the beneficiaries will receive a Sch 1041 K1 to report their share of the Trust income on their individual tax returns. If you are working with a lawyer, they will probably prepare the Trust tax return annually and should distribute the K1s to the beneficiaries that received income during the year.
But keep in mind, if you are able to distribute out the income generated in the trust annually, you will be saving tax dollars by not having it taxed in the trust.