What did the Federalists agree to in order to gain support for the new Constitution?

The Federalists agreed to add amendments to protecting basic rights in support of a new constitution.

The Federalists agreed to add a Bill of Rights to the Constitution that protected individual liberties and put limitations on government power.

Explanation:

During the debates over the ratification of the newly proposed Constitution, two groups emerged: The Federalists and the Anti-Federalists. One of the matters that these groups strongly disagreed with was the adding of a bill of rights to the Constitution: while the Federalists believed that the principle of Separation of Powers and the Checks and Balances principles upon which the Consitution was based was effective and enough to prevent abuses of powers, the Anti-Federalists believed that the Constitution alone was not enough, and that a bill of rights that specifically protected individual liberties and put limitations on government was necessary.

In the end, the Federalists agreed to add the Bill of Rights to the Constitution to get the Anti-Federalists' approval for the Constitution, and James Madison himself, a Federalist, ended up drafting the first 10 amendments.