In Arabic not so much: جار ‘neighbor’ comes from a root جور GWR, while جرى ‘to run’ looks similar but has different consonants (GRY).
Other Semitic languages have the ‘neighbor’ word for ‘foreigner, stranger’, e.g. Hebrew ger Syriac/Aramaic giyyura, Classical Ethiopic gəyyur (from GWR ‘to sojourn, dwell (together), live’), but GRY originally meant something like ‘to incite, stir up, attack’, compare in particular in Akkadian gerû(m)/garû(m) ‘to be hostile to, attack’. The meaning ‘to run’ is found only in Arabic, but could be developed from ‘to attack, stir up, agitate’ > ‘to cause to/make run’ > ‘to run’.
However, ‘be hostile to’ and ‘stranger’ are so similar (compare guest, host and hostile, all going back to the same word meaning ‘stranger’, https://www.etymonline.com/word/*ghos-ti-) that I think that there was an ancient connection between these words.