Discover king's name (5)
I believe the answer is:
learn
'discover' is the definition.
(I know that discover is a more specific form of discover)
'king's name' is the wordplay.
'king' becomes 'lear' (King Lear).
'name' becomes 'n' (common abbreviation e.g. on forms).
'lear'+'n'='LEARN'
(Other definitions for learn that I've seen before include "Acquire information" , "Ascertain" , "be taught a lesson" , "Become aware of" , "Take in" .)