Monopolise paintings by hot painter (7)
I believe the answer is:
hogarth
'painter' is the definition.
(I've seen this before)
'monopolise paintings by hot' is the wordplay.
'monopolise' becomes 'hog' (I've seen this in another clue).
'paintings' becomes 'art' (painting is a type of artwork).
'by' says to put letters next to each other.
'hot' becomes 'h' (abbreviation eg on taps).
'hog'+'art'+'h'='HOGARTH'
(Other definitions for hogarth that I've seen before include "William -, Eng. engraver (A Rake's Progress)" , "He depicted" , "Satirical 18th century painter" , "Engraver's" , "William ---, Brit. artist" .)