I have heard of a post, question, or meta process to request new tags for new anime, but I looked around and did not find it.
For future reference, any user with 150+ reputation, like you, can create tags. The problem we run into is that completely new users (starting at 1 rep) or users who only have the association bonus (starting at 101 rep) aren't quite there, and hence must resort to some sort of workaround. Any of the following are acceptable if you can't find a tag for a question you'd like to ask:
- Tag your question with retag (which you can also find by entering "anime" or "manga" into the tag field)
- Tag your question with any arbitrary tag, and flag your own post as "in need of moderator intervention" (provided that you have the requisite 15+ reputation)
- Or, honestly, just post your question in any manner you'd like. Our question volume is low enough that somebody with enough reputation is almost certain to notice and fix the tags on your post in short order.
Whichever you do, just be sure that the text of your question is explicit about which anime/manga/etc you're asking about.