Marciano to lose his footing and sway from side to side (4)
I believe the answer is:
rock
'sway from side to side' is the definition.
(rock can mean to sway or teeter)
'marciano to lose his footing' is the wordplay.
'marciano' becomes 'Rocky' (Rocky Marciano was a boxer).
'to lose his footing' means to remove the last letter (the bottom or 'foot' is lost from the word).
'rocky' with its final letter removed is 'ROCK'.
'and' acts as a link.
(Other definitions for rock that I've seen before include "possible danger at sea" , "Reel from" , "Brighton - (novel); - Hudson" , "Big stone - music" , "Gently move; boulder" .)