Like an old buffer's mistake involving uneven walk (8)
I believe the answer is:
blimpish
'like an old buffer's' is the definition.
(like the cartoon character Colonel Blimp)
'mistake involving uneven walk' is the wordplay.
'mistake' becomes 'bish' (term for a blunder or mistake).
'involving' is an insertion indicator.
'uneven walk' becomes 'limp' (to limp is to walk unevenly).
'bish' placed around 'limp' is 'BLIMPISH'.
(Other definitions for blimpish that I've seen before include "reactionary" , "(0f a elderly person) with incurably pompous and conservative views" .)