I am installing a new shower floor pan directly over an existing floor drain set in concrete. Is there an adapter I can use to connect the floor drain to the new shower drain in the floor pan?

Unless you want to tear up the floor and replace the floor drain with a "P" trap I would find a way to JB weld in a 2" piece of cast iron for a raiser and cring it up a few inches over the floor line before cementing and leveling the floor. You could also try to use epoxy to join the cast iron to 2" PVC and bring that up as a raiser,
Both methods will use the floor drain as a trap. The only draw back to this is the flooir drain isn't vented. This will work if it won't be inspected but if a permit's pulled you will have to run a vent out the roof or revent back to a dry vent. Good luck. Tom