Insuring title for property currently vested in an irrevocable trust is not hard, you just need to confirm the terms of the trust.
You'll need a signed copy of the full trust and any amendments. If the trustee has a signed memorandum/certificate of trust, take a look at that first. Many attorneys will prepare this short certificate which outlines the important parties and powers. A signed copy of this certificate can be relied upon. Some folks will record a copy of the certificate as an exhibit with the deed.
BTW I have found that trustees who do not have a certificate of trust are sometimes reluctant to give us a copy of the full trust. We just tell them we need it and wait until they comply.
I strongly suggest that you let your title underwriter walk you through your first trust transaction or two just to be safe. There are just a few issues to keep an eye on that you'll not want to miss.
We reviewed an interesting case last week in which two real properties were supposedly deeded into a trust. Turned out that one was and the other was not. The attorney who had prepared the deeds used the wrong legal description for one of the properties. The settlor is deceased so the successor trustee now has to raise an estate and will be signing the deed into our insured in the capacity of successor trustee and executrix of the estate.