Some start panicking while climbing, that’s not right (5)
I believe the answer is:
inapt
'not right' is the definition.
(I've seen this in another clue)
'some start panicking while climbing' is the wordplay.
'some' indicates a hidden word (some of the parts of the word are used).
'climbing' says the letters should be written backwards (in a down clue, letters climb up).
'tpani' is hidden within 'start panicking while'.
'tpani' reversed gives 'INAPT'.
'that's' acts as a link.
(Other definitions for inapt that I've seen before include "Inappropriate" , "It's clumsy" , "Not proper" , "Ill-chosen, not suitable" , "Far from fit" .)