Jamieson, Fausset and Brown on Hebrews 13:23

23. our brother Timothy--So Paul, 1Co 4:17; 2Co 1:1; Col 1:1; 1Th 3:2.

is set at liberty--from prison. So Aristarchus was imprisoned with Paul. Birks translates, "dismissed," "sent away," namely, on a mission to Greece, as Paul promised (Php 2:19). However, some kind of previous detention is implied before his being let go to Philippi. Paul, though now at large, was still in Italy, whence he sends the salutations of Italian Christians (He 13:24), waiting for Timothy to join him, so as to start for Jerusalem: we know from 1Ti 1:3, he and Timothy were together at Ephesus after his departing from Italy eastward. He probably left Timothy there and went to Philippi as he had promised. Paul implies that if Timothy shall not come shortly, he will start on his journey to the Hebrews at once.