Local to swear in town’s outskirts (6)
I believe the answer is:
tavern
'local' is the definition.
(I've seen this before)
'swear in town's outskirts' is the wordplay.
'swear' becomes 'aver' (synonyms).
'in' means one lot of letters goes inside another.
'outskirts' says to hollow out the word (remove centre letters) (I've seen 'outskirts of' mean this).
'town' with its centre removed is 'tn'.
'aver' placed into 'tn' is 'TAVERN'.
'to' acts as a link.
(Other definitions for tavern that I've seen before include "An old inn or public house" , "Alehouse" , "Old song: 'There is a ...... in the town, in the town'" , "Watering hole" , "Building with a bar" .)