Three different Hebrew words are used in the Old Testament to describe a mantle.
The first is “semiykah” – and it refers to a quilt or cover – and comes from a root word that referred to a bed (Judges 4:18).
The second is “m’iyl” – and it refers to an outer garment – typically a long tunic type article of clothing (Job 1:20). This word eventually referred also to the garments that priests wore.
The third is “addereth” – and referred to an interwoven garment. Interestingly, the word addereth can also mean “glory” or “magnificence” which would fit the story. Although this word is used with other Old Testament stories (see Josh. 7:24), it’s the ONLY one of the three terms used with Elijah and Elisha.
But, we have not been able to find any evidence that indicates passing a mantle was a common Jewish tradition that indicated a passing of power. It was an image of kinship, though, by the New Testament — as in the story of the returning of the prodigal son. Remember the father had the servant bring out and put on the son a robe, a ring, and some shoes (Luke 15:22).