While ndpu has correctly pointed you to context processors to solve the general problem, there doesn't really seem to be any need in this case.
You already have a direct relationship between the current user and the relevant Player: I assume that is a one-to-one. And the user
object is already passed to the template context by the default context processors, as long as you are using RequestContext (which you are, via the render
shortcut.) So, without any extra context at all, you can simply do this in your template:
{{ user.player }}
to get the player.