Town in SE Scotland on the banks of the River Tweed on the edge of which stands Neidpath Castle (7)

I believe the answer is:

peebles

(Other definitions for peebles that I've seen before include "Scottish borders town" , "Scots Borders town" , "Scottish border town on the 4 down" , "Scots county town on the river Tweed" .)

I've seen this clue in The Mirror.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.