I have classified تبع as a particle, as it does not decisively belong to any other part of speech; the تبع structure that it creates is unique in the language.
While its meaning is semantically close to English "of" — a preposition — its gendered forms suggest that it is not a preposition, which do not observe grammatical agreement.
Additionally, if it were the head of a prepositional phrase, the phrase should be preceded by اللي if modifying a definite noun — & the term only ever defines a definite noun.
On the basis of its genderedness alone, it should be either a noun — namely, a pronoun — with feminine & plural forms, or an adjective subject to gender & number agreement.
Normally, nouns can only modify other nouns via iḍāfa; in this structure, the modified term is overtly indefinite, while the final modifier is overtly definite:
However, in the تبع structure, the modified noun features the article, showing that there is no iḍāfa. Instead, the تبع structure is itself an iḍāfa structure in which تبع is the modified term; this is audible in the pronunciation of the feminine form.
Because of these reasons, the تبع structure is best understood as an adjective that can form iḍāfa, which is ordinarily impossible; the term observes definiteness agreement with the head noun — which must be definite in the تبع structure — but displays that agreement via iḍāfa.