Sharp practice finally admitted by Livingstone (4)
I believe the answer is:
keen
'sharp' is the definition.
('keen' can be a synonym of 'sharp')
'practice finally admitted by livingstone' is the wordplay.
'finally' indicates one should take the final letters.
'admitted by' indicates putting letters inside.
'livingstone' becomes 'ken' (Ken Livingstone is a famous UK politician).
The last letter of 'practice' is 'e'.
'e' put into 'ken' is 'KEEN'.
(Other definitions for keen that I've seen before include "express sorrow" , "devoted" , "Eager; dirge" , "Agog" , "Quick" .)