Sway from side to side and power into Olympic kayak finals (4)
I believe the answer is:
rock
'sway from side to side' is the definition.
(rock can mean to sway or teeter)
'power into olympic kayak finals' is the wordplay.
'finals' indicates one should take the final letters (the final letters).
The last letters of 'power into olympic kayak' are 'ROCK'.
'and' is the link.
(Other definitions for rock that I've seen before include "lull baby to sleep?" , "Move side to side" , "Brighton sweet?" , "startle" , "Style of music; shock" .)