In a serious manner (7)
'in a serious manner' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for earnestly that I've seen before include "Showing serious intent" , "Showing commitment" , "Zealously" , "with heart and soul" , "with gusto" .)
(Other definitions for sternly that I've seen before include "Cruelly" , "In serious way" .)