Put off by entering on the right-hand side (6)
I believe the answer is:
dexter
'on the right-hand side' is the definition.
(I've seen this before)
'put off by entering' is the wordplay.
'put off' becomes 'deter' (I've seen this before).
'by' becomes 'x' (multiplication sign).
'entering' means one lot of letters goes inside another.
'deter' going around 'x' is 'DEXTER'.
(Other definitions for dexter that I've seen before include "In heraldry, of or on the right side" , "Crime writer" , "Ted, right-handed cricket star?" , "far from sinister?" , "On the right-hand side in heraldry" .)