For the priesthood being changed (μετατίθημι), there is made of necessity a change also of the law. (Heb 7:12)
In a previous post, I discussed Heb 7:12 and the claim that this verse does not militate against the Aaronic Priesthood being part of the New Covenant; instead, as I demonstrated in that post, the Bible affirms the eternality of the Aaronic Priesthood.
To add to the discussion, here is the definition of μετατίθημι as provided by BDAG (Greek-English Lexicon of the New Testament and Early Christian Literature), the leading Koine Greek lexicon:
4860 μετατίθημι
• μετατίθημι by-form pres. 3 pl. μετατίθονται AcPl Ha 2, 26 (s. B-D-F §94, 1); fut. μεταθήσω Is 29:14; 1 aor. μετέθηκα; 2 aor. ptc. μεταθείς. Pass.: fut. 3 sg. μετατεθήσεται Is 29:17; 1 aor. μετετέθην (Hom.+) gener. ‘change (the position of)’.
1. to convey from one place to another, put in another place, transfer τὴν χεῖρα ἐπί τι transfer your hand to someth. B 13:5. W. acc. of pers. and indication of the goal μεταθέντες αὐτὸν ἐπὶ τὴν καροῦχαν they had him transferred to the carriage MPol 8:2. Pass.: of corpses μετετέθησαν εἰς Συχέμ they were brought back to Shechem Ac 7:16. W. indication of the place fr. which ἐκ τῶν βασάνων be removed from (the place of) torment Hv 3, 7, 6 (μετατίθημι ἐκ as a grave-ins fr. Amastris: JÖAI 28 Beibl. ’33, col. 81f no. 39). Of Enoch be taken up, translated, taken away (to heaven) Hb 11:5a; 1 Cl 9:3 (cp. Sir 44:16; Wsd 4:10); the act. in the same sense and of the same person Hb 11:5b (Gen 5:24).
2. to effect a change in state or condition, change, alter (Hdt. 5, 68 et al.; Jos., Ant. 15, 9; IAndrosIsis, Kyme 4: the νόμοι of Isis are not subject to alteration by humans) τὶ εἴς τι someth. into someth. (Esth 4:17s μετάθες τὴν καρδίαν αὐτοῦ εἰς μῖσος) τὴν τοῦ θεοῦ ἡμῶν χάριτα εἰς ἀσέλγειαν pervert the grace of our God to dissoluteness Jd 4. Pass. μετατιθεμένης τῆς ἱερωσύνης when the priesthood is changed, i.e. passed on to another Hb 7:12 (Jos., Ant. 12, 387 of the transfer of the office of high priest to another person).—Of a severe alteration in condition collapse μεγάλαι πόλεις μετατίθονται AcPl Ha 2, 25f.
3. to have a change of mind in allegiance, change one’s mind, turn away, desert mid. (Polyb. 5, 111, 8; 24, 9, 6; Diod. S. 11, 4, 6; 2 Macc 7:24 ἀπὸ τ. πατρίων.—ὁ μεταθέμενος in Diog. L. 7, 166 and Athen. 7, 281d [the latter without the art.] refers to Dionysius the Turncoat, who left the Stoics and adopted Epicureanism) ἀπό τινος εἴς τι from someth. to someth. μ. ἀπὸ τοῦ καλέσαντος ὑμᾶς … εἰς ἕτερον εὐαγγέλιον desert him who called you (and turn) to another gospel Gal 1:6 (cp. Hierocles 7 p. 429: there is to be no yielding to μεταβαλλομένοις ἐκ τῆς περὶ φιλοσοφίαν σπουδῆς εἰς ἑτέραν τινὰ τοῦ βίου πρόθεσιν; Just., D. 47, 5 ἀπὸ εὐσεβείας … ἐπὶ … ἀθεότητα; Field, Notes 188). ἀπὸ τῶν χαλεπῶν ἐπὶ τὰ δίκαια turn away from evil to good MPol 11:1 (cp. Just., A I, 45, 6 and D. 107, 2 al.).—M-M. TW.
The reference from Josephus cited by BDAG reads as follows:
Now as to Onias, the son of the high priest, who, as we before informed you, was left a child when his father died, when he saw that the king had slain his uncle Menelaus, and given the high priesthood to Alcimus, who was not of the high priestly family, but was induced by Lysias to translate (μετατίθημι) that dignity from his family to another house, he fled to Ptolemy, king of Egypt. (Antiquities of the Jews 12:387)
Obviously, in light of the biblical instances of μετατίθημι (discussed in the previous article on the eternality of the Aaronic Priesthood) and in light of the lexicographical evidence and from Josephus, nothing in the semantic domain of μετατίθημι, or Heb 7:12 itself, that poses any issues for Latter-day Saint theology.