At this point, it will take a moss killer to kill the moss.  Then you’ll rake out all the dead moss and reseed/overseed the area.  I’d suggest our “Shady” grass seed blend made up of grass types that thrive in shade.  You’ll also want to do a pH test so you’ll know how much pelletized limestone you’ll need to apply to correct (bring to neutral)  the pH of the soil.  Over time, soil becomes gradually acidic.  Tghe grass cannot thrive in acidic soil and starts to struggle ab die off.  Moss likes acidic soil and and takes over as the grass dies.  Had the pH of the area been kept neutral with occasional testing and lime applications, the moss would not have had the opportunity to take over.  Lime applications will NOT KILL THE MOSS now that it has taken hold.  Moss killer will kill it and correcting the pH will help the grass thrive and resist the moss.  Here’s a link that will walk you through how to do a pH test.  It is about as difficult as making a sandwich and well worth it.  https://blog.timesunion.com/gardening/can-your-lawn-pass-the-acid-test/7429/