Studio possibly suitable to hold paintings by bishop and queen? (9)
I believe the answer is:
apartment
'studio possibly' is the definition.
(studio is a kind of apartment)
'suitable to hold paintings by bishop and queen?' is the wordplay.
'suitable' becomes 'apt' (I've seen this before).
'to hold' is an insertion indicator.
'paintings' becomes 'art' (I've seen this before).
'by' means one lot of letters go next to another.
'bishop and queen?' becomes 'men' (two examples of chessmen).
'art'+'men'='artmen'
'apt' enclosing 'artmen' is 'APARTMENT'.
(Other definitions for apartment that I've seen before include "19 across" , "Flat (chiefly US)" , "property" , "Flat (mainly US)" , "place to live" .)