Using the GeoTiff module in TerrSet, you can export a .rst image along with a specific palette and/or Projection system.
If you created a specific palette in TerrSet and would like that palette to carry over to the export in a .tif format, save the .smp file with the same name as the image. When you export the file using GeoTiff, it will record the palette and open with the correct palette in ArcGIS.
If you have a user-defined reference system (.ref) created in TerrSet, you can export the parameters with the image. First, rename the .ref file to have the same name as the image. Second, edit the .rdc file for the image you are exporting so that the reference system has the name of the .ref file.
When the .tif file is opened in ArcGIS, it will have the palette from TerrSet, and/or the reference system.