Painter’s predicament entertaining bishop at home (7)
I believe the answer is:
holbein
'painter's' is the definition.
(Hans Holbein the Younger or Hans Holbein the Elder)
'predicament entertaining bishop at home' is the wordplay.
'predicament' becomes 'hole' (I've seen this in other clues).
'entertaining' is an insertion indicator.
'bishop' becomes 'B' (abbreviation used in chess).
'at home' becomes 'in' (similar in meaning).
'hole' enclosing 'b' is 'holbe'.
'holbe'+'in'='HOLBEIN'
(Other definitions for holbein that I've seen before include "Hans ---, painted Erasmus, More" , "Hans --, one of two related German painter" , "Hans -, German artist who painted Henry VIII" , "German painter at the court of Henry VIII" , "Hans --, one of two related German painters" .)