My sympathies for your loss.
The trust document itself will determine what action needs to be taken. Typically for revocable trusts involving spouses, upon the death of the first spouse (decedent spouse) the trust divides automatically into 2 trusts, the decedent's trust and the survivor's trust. Typically the decedent's trust is then irrevocable, and the surviving spouse is often the trustee. There is language in the trust that governs how much money can be disbursed by the trustee as to the decedent's trust - some will allow unlimited access, whereas others are limited to a monthly amount, or perhaps only the interest/income generated.
Upon the death of the second spouse, the proceeds are then disbursed according to the terms of the trust.
If the trust provides that the trust is to be irrevocable upon the passing of the first spouse, then that means that there is no division of trusts, and the surviving spouse, as trustee, has management over the funds which can be accessed for the purpose as stated in the trust. This type of estate planning is designed to protect the surviving spouse from undue influence- that during the vulnerable time after the first spouse dies, there may be concern that the surviving spouse would be encouraged to change the trust's beneficiaries or otherwise significantly alter the terms of the trust. By making it irrevocable, that concern is alleviated.
This article explains in detail:
So there is no need to set up another trust when one utilizes the joint trust as the trust is still in existence until the second spouse passes and the assets are distributed according to the trust.