Not solemn; perhaps just sleepy (9)
I believe the answer is:
somnolent
'sleepy' is the definition.
(I've seen this before)
'not solemn perhaps' is the wordplay.
'perhaps' indicates an anagram.
'not'+'solemn'='notsolemn'
'notsolemn' with letters rearranged gives 'SOMNOLENT'.
'just' acts as a link.
(Other definitions for somnolent that I've seen before include "drifting off" , "Lent moons (anag.)" , "Dozy" , "Sleepy, drowsy" , "falling asleep" .)