Our new neighbours (1)/ had been living in Arizona (2)/ since ten years before moving to their present house. (3)/ No error. (4)

Answer

3

Explanation

for will replace since because -
for (Prep.) indicates a length of time Since (Prep.) indicates a past time until a later time, or until now
Look at the examples given below:
I have lived in Bangalore for twenty-five years.
I had been living in Bangalore since 1964.
Hence, for ten years before moving to their present house is the right usage.