A sign that is still up after it no longer applies

Solution 1:

One word is out-of-date. It is an out-of-date sign. The sign is out of date.

You can also say that it is not up to date; it is not an up-to-date sign.

You can also say that the sign is no longer applicable, or that it no longer applies.

None of those expressions are single words, except for the hyphenated forms used as adjectives.

The single words mentioned in @GMB's comment are also applicable: obsolete, outdated, and defunct (though I probably would not apply defunct to a sign, myself).

Solution 2:

According to Oxford Dictionary Online, the term relic means

An object surviving from an earlier time, especially one of historical or sentimental interest.

While this definition does not explicitly reflect an intent to follow the outdated patterns, the religious connotation invites such an interpretation.