Most keen to have a right nuisance quiet at the outset (8)
I believe the answer is:
sharpest
'most keen' is the definition.
('sharp' can be a synonym of 'keen')
'a right nuisance quiet at the outset' is the wordplay.
'a right' becomes 'ar' (I've seen this in other clues**).
'nuisance' becomes 'pest' (I've seen this before).
'quiet' becomes 'sh'.
'at the outset' says to put letters next to each other.
'ar'+'pest'='arpest'
'arpest' put after 'sh' is 'SHARPEST'.
'to have' acts as a link.
(Other definitions for sharpest that I've seen before include "Most clearly defined or most cutting" , "may be the more knife-edged" , "Most keen and cutting" , "Most intelligent" .)