Bearing gifts we hear vaguely (8)

I believe the answer is:

presence

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'bearing' is the definition.
(I know that bearing can be written as presence)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for presence that I've seen before include "Impressive appearance" , "Charisma; mien" , "Demeanour" , "Being (significantly) there" , "Being there or close by" .)

I've seen this clue in The Globe and Mail.

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