Climber and I at each side of valley (3)
I believe the answer is:
ivy
'climber' is the definition.
(ivy is a climbing plant)
'i at each side of valley' is the wordplay.
'at each side of' means to remove the middle letters (I've seen 'at each side' mean this).
'valley' with its centre taken out is 'vy'.
'i'+'vy'='IVY'
'and' is the link.
(Other definitions for ivy that I've seen before include "Girl" , "Clinging vine" , "With holly, it's seasonally decorative" , "Girl's name; climber" , "The Hedera genus of evergreen climbers" .)