"It is their zone."
Translation:Het is hun zone.
In this case you use hun because it's possessive, the equivalent of the English 'their'. Hen means 'them'.
I'm happy to be corrected by a native speaker, but if I understood my teacher correctly, hun can also be used to mean 'them' when it's an indirect object without a preposition:
'Ik gaf de bal aan hen.' (I gave the ball to them.)
'Ik gaf hun de bal.' (I gave them the ball.)