Sakshi Sharma it is a sequel to heroes of Olympus as zeus got angry with Apollo in the war with gaea.
This answer contains spoilers… (view spoiler)[Around the end of Blood of Olympus, (after the fight with Giants) Zeus was apparently very angry with Apollo, and Apollo being made into a mortal (as far as I understand) would be his punishment for egging on Octavian and being swayed by flattery. So this would be set after Heroes of Olympus (hide spoiler)]
Emily Pretty sure it's a continuation of the PJO/HoO world/series, meaning set after Blood of Olympus
Sarah I think (not confirmed) that it will take place before the HoO series because that has so many stories that need to be told, especially the story of Octivian, there is something about him that makes him seem like more then is shown
Marian Atasha It's going to continue with the war of Gaea--since it's a sequel to the Heroes of Olympus.
Masumi Sera It's after. Apollo "disappeared" during the end of HoO, but it's only after that they actually figure out the reason of his disappearance, hence the Trials of Apollo.