'living a life, which embraced tradition,' Which part of speech is the underlined word?

'Which' here introduces a relative clause modifying 'life'. It functions as a relative pronoun — replacing/referring back to 'life' as the subject of the embedded clause 'which embraced tradition'. Relative pronouns (who, which, that, whose, whom) connect clauses while functioning grammatically as pronouns. It is not a determiner here (it's not modifying a noun in the clause), not an adjective, not an adverb.