It's unusual to defun within a function. If you just want expat available while executing expand-pattern, you should use use letrec:
(defun expand-pattern (pattern)
(letrec ((expat (lambda (parents expr)
(pcase expr
((or (pred stringp)
(pred numberp)) (mapcar (lambda (parent)
(cons expr parent))
parents))
(`(and ,first) (funcall expat parents first))
(`(and ,first . ,rest) (funcall expat (funcall expat parents first)
(cons 'and rest)))
(`(or . ,args) (apply #'append
(mapcar (lambda (arg)
(funcall expat parents arg))
args)))
(_ (error "unknown %S" expr))))))
(mapcar (lambda (tokens)
(mapconcat (lambda (token)
(format "%s" token))
(reverse tokens)
""))
(funcall expat '(()) pattern))))
This way, the binding of expat doesn't live beyond the function.
It looks like what you're doing is a 'reduce' type of operation - you may find it worthwhile to look into cl-reduce and related functions.