If you are using v16.0.3 and wanting to add the new GDA 2020 datum, you will firstly need to download the two .GSB (grid shift files for NTv2 conversions) files available from the v16.0.3 maintenance patch download web page. The files need to be placed into the MapInfo Pro v16 installation program directory (by default under C:\Program Files\MapInfo\Professional)
Next, the following lines of text below will need to be added to the MAPINFOW.PRJ file (this file is located by default under the installation directory C:\Program Files\MapInfo\Professional). The .PRJ file can be opened and edited using a text editor such as Notepad++. Once added, save the changes to the .PRJ file and the new projection should then be available in MapInfo Pro.
A sample default MAPINFOW.PRJ file is attached here which contains the new datum code added to it for reference purposes.
"--- Map Grid of Australia 2020 (MGA2020) ---"
"MGA2020 Zone 47", 8, 1028, 7, 99, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 48", 8, 1028, 7, 105, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 49", 8, 1028, 7, 111, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 50", 8, 1028, 7, 117, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 51", 8, 1028, 7, 123, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 52", 8, 1028, 7, 129, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 53", 8, 1028, 7, 135, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 54", 8, 1028, 7, 141, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 55", 8, 1028, 7, 147, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 56", 8, 1028, 7, 153, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 57", 8, 1028, 7, 159, 0, 0.9996, 500000, 10000000
"MGA2020 Zone 58", 8, 1028, 7, 165, 0, 0.9996, 500000, 10000000