I have a bunch of templates I made in Gist form so people can discuss them at the bottom.
We like to copy these files and paste them into a repo and make an addon th
Is it possible to fork a Gist to Repo via the GitHub site or client?
Not directly.
You can try to add a bookmarklet like "Fork your own Gist".
But there won't be any pull request feature.
If that becomes an issue, it is better to create a full-fledged GitHub repo out of your Gist collection of files.
(As in "Transfer gist repo into a github one").
Since my original answer in 2014, the ability to fork a gist (as mentioned in Bruno-Bronosky's answer) was added (around 2015).
Each gist indicates which forks have activity, making it easy to find interesting changes from coworkers or complete strangers.
See for instance "A basic collaboration workflow on Gist" (Apr. 2015) from Giovanni Cappellotto (potomak on GitHub).
Again, there is no direct pull request supported (still valid in 2020).