You could compute your GS knowing your TAS, but then you must also know your exact wind. At any moment. Nobody does.
It sounds like you fly a jet. On those, the airdata computer gets IAS, OAT, pressure altitude, computes the TAS from the foregoing, then gets the heading (from the fluxgate compass system), gets the track and GA (from the FMS i.e. INS or GPS), and calculates the wind vector from those.
One can get the same in GA (
example) but it's hardly worth it for the cost.