Where climbers go on horseback with notices about river (7)
I believe the answer is:
upwards
'where climbers go' is the definition.
'on horseback with notices about river' is the wordplay.
'on horseback' becomes 'up' (up can mean up on a horse).
'with' becomes 'w' (abbreviation).
'notices' becomes 'ads' (advertisements).
'about' means one lot of letters goes inside another.
'river' becomes 'r' (abbreviation for river).
'ads' going around 'r' is 'ards'.
'up'+'w'+'ards'='UPWARDS'
(Other definitions for upwards that I've seen before include "in direction of ceiling" , "To a higher position" , "Towards a higher level" .)