Anxious to get Livingstone out of the way! (4)
I believe the answer is:
keen
'anxious' is the definition.
(I've seen this before)
'livingstone out of the way' is the wordplay.
'livingstone' becomes 'Ken' (politician Ken Livingstone).
'out of' is an insertion indicator (some letters on the outside of others).
'the way' becomes 'e' (Compass direction - East).
'ken' enclosing 'e' is 'KEEN'.
'to get' acts as a link.
(Other definitions for keen that I've seen before include "Quick" , "Anxious" , "Agog" , "Fervent" , "cry" .)