What did the Founding Fathers promise they'd do
to gain support for the constitution?

They promised to sign the Bill of Rights and include it on the Constitution.

Explanation:

At the time of the sanction of the Constitution, a large political pressure group was formed with the objective of preventing said norm from coming to light. These people, the so-called Anti Federalists, believed that the formation of a one-man government based on the President would be the starting point for the development of a new tyranny. Therefore, they began to carry out lobbying actions to prevent the Constitution from being approved.

In view of this, the Founding Fathers guaranteed the signing of the Bill of Rights, a series of 10 amendments to the Constitution which would include a series of non-derogable rights for American citizens, which would guarantee their freedoms and limit the unlimited exercise of prerogatives by part of the federal government.

The Founding Fathers gained support for the Constitution by promising a Bill of Rights would be established. Had the Federalists not agreed to add a Bill of Rights later, the Constitution likely would not have been approved by the states.

me on my last question.