Zeno's Republic was almost certainly written as a response of some kind to Plato's famous work. What differences between Plato's ideal society and his Stoic utopia did Zeno wish to highlight and in what way was writing the work with such obvious parallels intended to support his beliefs?
▻ THE TEXT
It is true that the text of Zeno's 'Politeia' has been lost but there is a large collection of surviving fragments to be found in Diogenes Laertius, Philodemus, Clement of Alexandria, St John Chryostom and others. The fragments are all cited in the first volume of Arnim's 'Stoicorum Veterum Fragmenta'. 'Politeia' is unlikely to have been the title Zeno himself gave to the work.
▻ CLASS STRUCTURE
Plato's 'Republic' contains three classes or kinds of person, and not exclusively the wise. Wisdom resides exclusively in the philosopher-rulers. There is some indication by contrast that Zeno's ideal polis or state is a polity of the wise.
▻ PAST OR FUTURE
The evidence is not clear but the majority view is that Zeno projects his ideal polis or state into the future; it is not a description of lost, past political conditions. The status of Plato's 'Republic' is, of course, a matter of great controversy. Did he think it achievable ? Unlikely, because it is perfect and humanity has no part in perfection. Is it a thought-experiment of what political perfection would be like. Not only do views vary but they are likely to continue to do so.
Plato talks only of a single polis - the kallipolis - though he does not exclude the possibility of a plurality of perfect polities. He just says nothing about it. Some commentators have thought that Zeno just one ideal polis in mind, others that he envisaged a plurality of polities or even a 'world state' (to use an anarchonistic expression). Here I think we just have to say we don't know whether Zeno had one polity, several polities or all political communities in mind as possible embodiments of the ideal polis.
▻ HOW TO GET THERE
Plato talks of the possibility that rulers should become philosophers, and the kallipolis come into existence that way. Zeno gives no indication of how the ideal polis or state is to come about.
Plato is much concerned in the 'Republic' that sexual relations should be controlled in the interest of not diluting the excellence of the class of philosopher-rulers. Zeno appears more relaxed and less inclined to control; this would make sense on the assumption that his ideal polis or state was a polity of the wise. If all are wise, there is no risk of generational decline through intercourse with the unwise.
▻ CIVIC LIFE
The ideal polis or city is to have no temples, law courts or gymnasia. Gymnasia were perhaps excluded because the wise would not be concerned with such lowly things as the condition of own bodies; their minds were on higher things. Law courts were unnecessary presumably because the wise cold sort out disputes for themselves. Temples would be imperfect constructions, unworthy of the gods. There is every reason to suppose that Plato retained gymnasia (Rep., III, 403d ff.). And since he wants, not to eliminate a belief in the gods but only to purge religious beliefs of false elements, we may suppose that temples were not abolished in the kallipolis. Plato's view of the situational insight that the philosopher-rulers possess by virtue of their acquaintance with the Forms (eide) suggests that their wisdom would supersede the need for law courts.
Other details, such as coinage, which Plato said nothing about in the 'Republic', could be explored but Zeno's ideal polis or state has been outlined here from the available evidence.
H. von Arnim, 'Stoicorum Veterum Fragmenta', vol 1, Bibliotheca Teubneriana, 1903.
H. C. Baldry, 'Zeno's Ideal State', The Journal of Hellenic Studies, Vol. 79 (1959), pp. 3-15.