John Lightfoot on Luke 2:37

[Departed not from the Temple.] I. It may be doubted whether any women ever discharged any office in the Temple: some think they did. But that which they allege out of 1 Samuel 2:22, concerning the women that assembled at the door of the tabernacle of the congregation, is quite another thing from any public ministering, if we will admit the Targumist and the Rabbins for expositors. So Exodus 38:8, women assembling by troops at the door of the tabernacle of the congregation. The Targumists both here and in the place before quoted have it, women that came to pray...

It is apparent, that women were wont to come from other parts to the tabernacle for devotion's sake, not to perform any ministry. So this Anna, by birth of the tribe of Aser, had changed her native soil, and fixed her abode at Jerusalem, partly for devotion, that she might be the more at leisure for praying in the Temple, and partly as a prophetess, that she might utter her prophecies in the great metropolis.

II. She departed not from the Temple; that is, not in the stated times of prayer: according as it is commanded Aaron and his sons, Leviticus 10:7; "Ye shall not go out from the door of the tabernacle." Where Siphra, fol. 24. 2, not in the time of their ministry.