Sincerely (9)
(Other definitions for earnestly that I've seen before include "Showing serious intent" , "Relent, say, in sincere and serious manner" , "with heart and soul" , "with gusto" , "In all seriousness" .)
'sincerely' is the definition.
(thesaurus)
This is all the clue.
(Another definition for genuinely that I've seen is " Truly".)