Turning, cats maybe run: one could climb this? (10)
I believe the answer is:
stepladder
'one could climb this?' is the definition.
'turning cats maybe run' is the wordplay.
'turning' says the letters should be written in reverse.
'cats maybe' becomes 'pets'.
'run' becomes 'ladder' (both can mean a rip in tights).
'pets' reversed gives 'step'.
'step'+'ladder'='STEPLADDER'
(Other definitions for stepladder that I've seen before include "Painter's mate" , "Domestic climbing aid" , "Portable climbing aid" , "Decorator's platform" , "Portable means of ascent" .)