Fairly small-minded about queen (6)
I believe the answer is:
pretty
'fairly' is the definition.
(I know that fairly can be written as pretty)
'small-minded about queen' is the wordplay.
'small-minded' becomes 'petty' (synonyms).
'about' means one lot of letters goes inside another.
'queen' becomes 'r' (abbreviation for regina, e.g. in ER ).
'petty' enclosing 'r' is 'PRETTY'.
(Other definitions for pretty that I've seen before include "Fair - fairly" , "sweet" , "charming to look at" , "Fairly - good-looking" , "pulchritudinous" .)