FlightGear has support for this, but obviously only for aircraft which have a corresponding GPS and the required autopilot installed, so you need to pick the right aircraft, too. Basically, the GPS outputs will then be linked to the CDI of the VOR/HSI/RMI and can be slaved to the autopilot, too.
All this is working through the property tree, so the CDI or the autopilot don't really care about where the inputs are coming from, so you could even come up with your own radio navigation equipment, i.e. a "
microwave landing system" (implemented in Nasal) and slave it to the CDI/autopilot, this could also be done for RNAV/IRS obviously.
IIRC, there are a number of aircraft such as the C182rg, the b1900d and some others, that come with fully functioning GPS support. But you may need to check this info, because I haven't tested this in a while, so I may be wrong about the current status.