C-c ~ (slime-sync-package-and-default-directory): When run in a buffer with a lisp file it will change the current package of the REPL to the package of that file and also set current directory of the REPL to the parent directory of the file.

On success it will display

package: NEW-PACKAGE-NAME  directory: ~/

 in the minibuffer, or

package: CURRENT-REPL-PACKAGE (package :foo doesn't exist)  directory: ~/

when specified in the file package doesn’t exist yet.