Adam Clarke on Hebrews 13:23

Know ye that our brother Timothy - The word ἡμων, our, which is supplied by our translators, is very probably genuine, as it is found in ACD*, ten others, the Syriac, Erpen's Arabic, the Coptic, Armenian, Slavonic, and Vulgate.

Is set at liberty - Απολελυμενον· Is sent away; for there is no evidence that Timothy had been imprisoned. It is probable that the apostle refers here to his being sent into Macedonia, Phi 2:19-24, in order that he might bring the apostle an account of the affairs of the Church in that country. In none of St. Paul's epistles, written during his confinement in Rome, does he give any intimation of Timothy's imprisonment, although it appears from Phi 1:1; Col 1:1; Plm 1:1; that he was with Paul during the greatest part of the time.

With whom, if he come shortly, I will see you - Therefore Paul himself, or the writer of this epistle, was now at liberty, as he had the disposal of his person and time in his own power. Some suppose that Timothy did actually visit Paul about this time, and that both together visited the Churches in Judea.