The Story Guide (linked in my signature or any recent event thread) has a list of all goals and triggers in 2 pages.
(after you finish Kaz's Five, the next goal is called But We Just Met - complete this goal and Knock On Wood from Blythewood part 3 to trigger Team Azalea/Lila goals.)
It gets a little bit complicated around now... so many parts of the story are intertwined.
1. In order to open the goal line for The Troll Sparring pit, you need to complete #8 "Home At Last" from story arc called "Kaz Returns from Blythewood" to trigger these goals.
2. You have to complete the Faerie Bridge to start that story arc.
3. To get the Faerie Bridge you must have completed Start of Something Beautiful from The Faerie Workshop story arc
4. To get to the Faerie Workshop you must have completed the Plume Hive story arc to trigger these goals
and on it goes...
It's really helpful to see it all layed out in the
Story Guide - you likely want page 2.
You'd need to post your goals so I can where you're up to in order to help you more. If you can use the
Help Me thread (as it's more accessible and the better place to post) that would good as your question isn't directly related to this part of the story.