I would suggest hiding it if there are no valid coupons which can be applied to it.

As per this article,

27 % of users abandoned carts to go search for a coupon codes

and if there are no valid coupon codes available, there is a possibility you might lose your users as they might not return.

That said, you can use that space to get people to sign up for your newsletter and increasing your reach by offering them discounts via email as shown by this article. To quote the article

Alibris does one better by providing the ability to enter an email address right on the page, as opposed to Office Max which makes you hunt for the email subscribe area.

I would suggest hiding it if there are no valid coupons which can be applied to it.

As per this article,

27 % of users abandoned carts to go search for a coupon codes

and if there are no valid coupon codes available, there is a possibility you might lose your users as they might not return.

That said, you can use that space to get people to sign up for your newsletter and increasing your reach by offering them discounts via email as shown by this article. To quote the article

Alibris does one better by providing the ability to enter an email address right on the page, as opposed to Office Max which makes you hunt for the email subscribe area.

On reflection of what Marjan Venema pointed out, It might be better practice to show that there are currently no active coupon codes which the user can potentially use as that would reduce the confusion about if a old coupon code found was valid or not.

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