Discover king's name (5)
I believe the answer is:
learn
'discover' is the definition.
(I know that discover can be written as learn)
'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" .)