That is the Great Seal of the United States, which is governed by Public Law 91-651, Title 18 of the United States Code.
Under that law, it prohibits usage that may be "reasonably calculated to convey, a false impression of sponsorship or approval by the Government of the United States or by any department, agency".
The seal is used for President Trump's official post-presidential office. Since a former President is allowed to open an office to coordinate their post-presidential activities under the Former Presidents Act, the office is "sanctioned" by the government. There is nothing prohibiting former Presidents from using the seal.
The establishment of the office is customary. The 1958 Former Presidents Act provides taxpayer-funded allowances and office staff to former presidents to help them answer mail, manage speaking requests and handle other informal public duties. The act provides funding for salaries, employment benefits, office space, equipment, supplies and materials, and more.
President Barack Obama also uses the seal in the logo for his post-presidency office.
As is the case for President George W. Bush:
Presidents Jimmy Carter and Bill Clinton don't have logos for their offices as they operate out of the Carter Center and the Clinton Foundation, respectively.
Further details regarding post-presidency offices from Sun-Sentinel:
Many former presidents have post-presidency offices, including George W. Bush, Barack Obama and Bill Clinton. None of them used the title of “former president” to name their offices because the phrase is not exclusive to their presidency, the same way it is not exclusive to Trump’s. Instead they simply used their names for their offices’ title.