Well, Roman legions were pretty busy putting out fires all over the place. Varus and all his legions were pretty famously destroyed by Arminius in the Teutoberg Forest in 9 CE.

I can't speak to what may have been happening in Asia, the Americas, Polynesia, and Africa, but in Rome, despite the relative peace of the Pax Romana, or the Pax Augusta, there were still a few rebellions and minor conquests in Illyria, Germania, Numidia, Thrace, Gaul...

Do you mean solely in Jerusalem and its environs? What qualifies as a "major" conflict? My feeling is that if you die in a minor conflict you're just as dead as in a major one, but is there a particular number of belligerents necessary to qualify as major?

Long story short: Yes. From 17 AD until 23 AD, China had a revolution, then a civil war from 23 AD until 25 AD

Short story long: The Xin Dynasty (新朝) ruler Wang Mang (王莽) had usurped the imperial throne in 9 AD. Two major forces, the Lüling Army (綠林軍 or Army of Mount Lüling) and the Red Brow Army (赤眉軍 or Red Brows Army, because they dyed their eyebrows red), both led by members of the Liu family of the Han Dynasty (漢朝), were highly instrumental in overthrowing the Xin Dynasty. However, after 6 years (17 AD - 23 AD) of restoring power to the Liu family, the two armies fought each other for the throne for another 2 years (23 AD - 25 AD)

The Han Dynasty (206 BC - 220 AD) can be split into a first half and a second half. The first half of the dynasty (206 BC – 9 AD) is sometimes known as the Western Han (西漢) or Former Han (前漢). This second half of the dynasty (25 AD - 220 AD) is sometimes known as the Eastern Han (東漢) or the Latter Han (後漢). The western and eastern distinctions point to the Western Han placing its capital further west at now-Xi'an, then known as Chang'an (長安), and the Eastern Han placing its capital further east at Luoyang (洛陽)