Weakens in one small part of the country (5)
I believe the answer is:
wilts
'weakens' is the definition.
(wilting is a kind of weakening)
'one small part of the country' is the wordplay.
I cannot quite understand how this works, but
'one' could be 'i' (Roman numeral) and 'i' is found within the answer.
'small' could be 's' (abbreviation - e.g. clothes size) and 's' is located in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
'in' is the link.
Can you help me to learn more?
(Other definitions for wilts that I've seen before include "Count[r?]y" , "(Of foliage) goes limp" , "loses vigour" , "part of the kingdom" , "A county (abbr.); suffers from 1" .)