This paperback was read a long time, possibly late seventies to mid eighties. Some hidden society who guard and monitor various portals that lead to Earth, however the portals are staggered throughout time, Ancient Greece, mid Europe during the Black Death, American civil war and others I can't remember.
The portals lead to other worlds and societies but a lot have been overrun by these vicious, intelligent man size insects who call themselves the Na. They are hive creatures but have placid Queens, they are led by Sires who are like supreme warlord emperors.
There was one section where a rogue explorer Na finds an empty moon and decides to use it to set himself up as a Sire, he steals a number of royal eggs and kills off any males who hatch so he will end up with a load of females to breed with.
He somehow ends up with some Earth bad guys who've stumbled across the portal network and are a-plundering across time and space. They give him some corned beef and the protein causes him to transform too rapidly into full Sire mode (I think this kills him).
In another part of the story some guy in Ancient Crete or Greece gets an alert a Na is coming through a portal and he blasts it with a device that transmits "ANGER OF A SIRE" and then has to tow the body out to sea in darkness and weigh it down.