im pretty sure it has to do with talking with the announcer dude in the arena and the doctor lady in medbay (havent played this in a while but thats about it, I think)
Talk to Eliza/ doctor Quinn to continue that part of the quest. If you have already go to the greenhouse (the place you get Apple's) and get the plant you need there.
Also check your tasks under the me button. Lots of other neat things there too.
