ar- prefix would be royal.
thibin is a piper, i.e., someone who plays a flute to make music with.(Instead of that other contraption that's used to simulate someone stepping on a cat's tale, but I digress. :) )
So, would a royal piper be arthibin? Or would there be some kind of mutation. (That's something I just haven't been able to wrap my head around. :( )
I would prefer to base the results on "royal musician", but I can't find a Sindarin word for musician.