With an evenly balanced disposition, starting to speak your mind as the UK went in 1965 (9)
I believe the answer is:
symmetric
'with an evenly balanced disposition' is the definition.
'starting to speak your mind as the uk went in 1965' is the wordplay.
'starting to' indicates taking the first letters.
'as the uk went in 1965' becomes 'metric' (UK adopted metric units in 1965).
The initial letters of 'speak your mind' is 'sym'.
'sym'+'metric'='SYMMETRIC'
(Other definitions for symmetric that I've seen before include "Equally balanced" , "Regular" .)