I got the Emerald Necklace while doing the quest “A Fin of Every Kind” in Azj-Kahet, but I can’t accept the quest from the necklace. It says that I do not meet the requirements.
I am level 80, and I tried accepting it while I was on A Fin of Every Kind, I tried accepting it after I had finished that quest, and I tried deleting the necklace and re-looting it (it now won’t drop).
What do?
Can’t help. but im stuck on the same situation as you. I have done the quest 1. A Fin of Every Kind but can’t use the necklace as says i dont meet the pre-requisites. I’ve also done ever other quest in the zone, this is the last group of quests for the zone to complete (except for “Those are Chitin words”.
i jumped on an alt and was able to pick up the quest “https://www.wowhead.com/object=443995/familiar-looking-appendage” from an item in the lake near a shore. Took it back to Al’kubian and could continue the rest of the quest chain. Now completed all quests in the zone, just not all on 1 toon 
Same problem here. Looks like the 11.0.7 update broke this quest.
I now have at 55, 71 the quest appear in the lake on my main toon who had a problem yesterday - hopefully working for you both now too!
The quest apparently got absorbed or redirected to “familiar looking appendage” with the last patch. I had to disable all my addons and then the new quest appeared for me and I got the completed quest no problem.
I am also having the same problem, currently have finished the quest “A fin of Every Kind” and picked up “emerald necklace” it is in my backpack however upon clicking on the item to start the quest, it tells you “you have already completed this quest” which i know i havent because it still appears as a questline in the achievement guide and still shows “!” Quest marker for the “That’s pretty gross quest” is there any fix for this?
it is literally one of the last things i need to do in that zone to have fully completed it but have given up trying after finding out this was bugged.