I would like to add a new tag to Board & Card Games Stack Exchange, but of course it requires 1500 reputation. This will be pretty hard to get on this site since it is in beta. Is there an acceptable way for me to request a tag be added by someone with 1500 reputation?
On beta sites like Boardgames, you can already create tags when you have 150 reputation. If you don't have the necessary reputation, you can ask on the site's own Meta to have the tag created, but you need to provide good arguments to do so. Other alternatives are the site's chat, or ping another high-rep user who was involved in the question.
Tags cannot be created unless there are questions existing that fit the tag. For Boardgames.SE, if there is a particular game that you are interested in, but there aren't any questions about that game, you won't find a tag for it yet.
If there are already questions about that game, but no tag yet, you can ask about creating that tag on meta. If there aren't any questions yet, but you have a question, feel free to ask it. Most likely, a high-rep user will come by and create the tag after you ask the question.