He can make one ill (6)
I believe the answer is:
lionel
'he' is the definition.
'make one ill' is the wordplay.
'make' indicates an anagram.
'one'+'ill'='oneill'
'oneill' with letters rearranged gives 'LIONEL'.
'can' is the link.
(Other definitions for lionel that I've seen before include "Guy" , "- Bart, (Oliver!)" , "Blair possibly" , "Boy" , "-- Bart; -- Richie" .)