Gain knowledge of Shakespearean king close to Regan (5)
I believe the answer is:
learn
'gain knowledge' is the definition.
('learn' can be a synonym of 'gain knowledge')
'shakespearean king close to regan' is the wordplay.
'shakespearean king' becomes 'lear' (I've seen this before).
'close to' indicates one should take the final letters (the close/ending of).
The last letter of 'regan' is 'n'.
'lear'+'n'='LEARN'
'of' acts as a link.
(Other definitions for learn that I've seen before include "Study - find out" , "Commit to memory" , "what pupils do in schools" , "Con" , "teach illiterate" .)