He painted bishop with bad back gulping too much cold water (10)
I believe the answer is:
botticelli
'he painted' is the definition.
(15th-century painter Sandro Botticelli)
'bishop with bad back gulping too much cold water' is the wordplay.
'bishop with' becomes 'b' (I've seen this in other clues).
'bad back' becomes 'lli' (I am not sure about this - if you are sure you should believe this answer much more).
'gulping' is an insertion indicator (gulp can mean to swallow or consume).
'too much' becomes 'ott' (short for 'over the top' - informal British).
'cold water' becomes 'ice'.
'b'+'lli'='blli'
'ott'+'ice'='ottice'
'blli' going around 'ottice' is 'BOTTICELLI'.
(Other definitions for botticelli that I've seen before include "who painted?" , "Italian painter of The Birth of Venus, d. 1510" , "Florentine C fifteen-sixteen artist (Primavera)" , "Famous Italian" , "Italian painter, 1445-1510" .)