Like the beauty queen - no 'queen', being most small-minded? (8)
I believe the answer is:
pettiest
'most small-minded?' is the definition.
('petty' can be a synonym of 'small-minded')
'like the beauty queen no queen being' is the wordplay.
I cannot quite see how this works, but
'being' could be 'pet' (pet is a kind of being) and 'pet' is located in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for pettiest that I've seen before include "most small-minded?" , "Most paltry or trivial" .)