Solemn girl's first to have wild party! (5)
I believe the answer is:
grave
'solemn' is the definition.
(grave can mean solemn or serious)
'girl's first to have wild party' is the wordplay.
'girl's first' becomes 'g' (1st letter of 'girl').
'to have' is a charade indicator (letters next to each other).
'wild party' becomes 'rave' (a dance party).
'g'+'rave'='GRAVE'
(Other definitions for grave that I've seen before include "Stern, serious" , "Weighty" , "In which to lay a corpse" , "Grim-faced" , "Last resting place" .)