King takes courses, becoming great in English verse (5)
I believe the answer is:
keats
'great in english verse' is the definition.
(poet John Keats)
'king takes courses' is the wordplay.
'king' becomes 'k' (abbreviation for king in chess).
'takes courses' becomes 'eats' (as in to eat courses of a meal).
'k'+'eats'='KEATS'
'becoming' acts as a link.
(Other definitions for keats that I've seen before include "English romantic poet, d. 1821" , "Grecian Urn poet" , "Author of the poem Ode to a Nightingale, d. 1821" , "Early 19th century poet" , "One of two born together" .)