Adam Clarke on Hebrews 13:24

Salute all them that have the rule over you - Salute all your leaders or guides, τους ἡγουμενους ὑμων. See on Heb 13:7 (note) and Heb 13:17 (note).

And all the saints - All the Christians; for this is the general meaning of the term in most parts of St. Paul's writings. But a Christian was then a saint, i.e. by profession a holy person; and most of the primitive Christians were actually such. But in process of time the term was applied to all that bore the Christian name; as elect, holy people, sanctified, etc., were to the nation of the Jews, when both their piety and morality were at a very low ebb.

They of Italy salute you - Therefore it is most likely that the writer of this epistle was then in some part of Italy, from which he had not as yet removed after his being released from prison. By they of Italy probably the apostle means the Jew's there who had embraced the Christian faith. These salutations show what a brotherly feeling existed in every part of the Christian Church; even those who had not seen each other yet loved one another, and felt deeply interested for each other's welfare.