Malachi was the last of the minor prophets and modern English translations place the minor prophets at the end of the OT. But in both the Hebrew Tanakh and the Greek Septuagint, the Prophets were followed by the Writings (the Hagiographa), and these included works later than Malachi -- such as Esther, 1 and 2 Chronicles, Daniel, and in the case of the Septuagint, Hellenistic works of the Apocrypha such as Judith, Tobit, and so forth. Although Daniel is today placed alongside the major prophets in English translations, in the Tanakh it was reckoned among the Writings even though it was every bit a "prophetic" work as Isaiah, Ezekiel, etc. This is because the canon of the Prophets was already established by the time Daniel was published (around 164 BC), and the only division of the Tanakh still open at that time was the Writings (which was not finally set until around AD 200 when Esther was finally universally accepted and the deuterocanonicals excluded).
The history of the so-called intertestamental period is best filled in by 1 and 2 Maccabees (along with 3 Maccabees, which concerns a time somewhat earlier than the Antiochean persecution) and Josephus, though the Great Vision of Daniel, ch. 11 also relates these events in symbolic language. The intellectual and religious climate however is best glimpsed by reading such works as Sirach, Wisdom, 4 Maccabees, 1 Enoch, the Testaments of the Twelve Apostles, the Testament of Moses, Joseph and Asenath, the various treatises and tractates of the Dead Sea Scrolls, and the writings of Philo of Alexandria. These works certainly help bridge the "gap" between the OT and the NT.