Solemn person starts to offer wise lessons (3)
I believe the answer is:
owl
'solemn person' is the definition.
(owl can mean a wise or solemn person)
'starts to offer wise lessons' is the wordplay.
'starts to' says to take the initial letters.
The initial letters of 'offer wise lessons' is 'OWL'.
(Other definitions for owl that I've seen before include "Creature" , "Athena's bird" , "Hooting bird" , "Lear's loved a Pussy-cat" , "paragon of wisdom?" .)