Old S American resident's mad to avoid climb-down (5)
I believe the answer is:
incan
'old s american resident's' is the definition.
(the Inca were a South America people)
'mad to avoid climb-down' is the wordplay.
'mad' becomes 'incandescent' (mad with rage).
'to avoid' suggests deleting specific letters.
'climb-down' becomes 'descent' (climbing down).
'incandescent' with 'descent' taken away is 'INCAN'.
(Other definitions for incan that I've seen before include "Relating to South American civilisation" , "Pachacuti for example" , "Relating to a pre-conquest people of Peru" , "See old South American" , "doing time?" .)