Provided straps to one refusing to climb (6)
I believe the answer is:
reined
'provided straps' is the definition.
(reins are strapped onto something)
'one refusing to climb' is the wordplay.
'one refusing' becomes 'denier' (someone denying or refusing something).
'to climb' says the letters should be written backwards (I've seen 'climbing' mean this (in a down clue, letters climb up)).
'denier' written backwards gives 'REINED'.
'to' acts as a link.
(Other definitions for reined that I've seen before include "Pulled in, checked progress" , "Stopped or slowed a horse" , "Restrained" .)