Question

Which of these pronouns is third-person plural possessive

Answer 1

Third-person means the speaker is referring to people separately rather than directly to them. For example, one might talk about 'them', or how 'it' was affected, maybe how 'she' did this or 'he' did that. You are not saying 'you' did this or 'we' have done that, but rather you are speaking of them rather than to them.

The definition of 'plural' is common knowledge. You use plural pronouns to refer to multiple things rather than just one. You're talking about 'those' apples, not 'the' apples.

Possessive is what it sounds like. You posses something, it's yours. The bread is 'theirs' and the book is 'his'. Maybe the tea is 'hers' and perhaps the pen is 'yours'.

Knowing all of this, what pronoun refers to a person separately rather than speaking directly to them, is plural, and suggests possession of something?

Answer 2

Third person plural pronoun is THEY.
If you want to create a possessive pronoun out of that one, that would be THEIRS. 
Possessive pronouns, as the name itself says, determine some kind of possession. For example:
Is this books yours? - No, it's theirs.