How to access enum properties in EL?

Since Primefaces 6.0 you can also use PrimeFaces importEnum (Before that import was in "Primefaces Extensions").

https://www.primefaces.org/showcase/ui/misc/importEnum.xhtml

This, as commented by Sazzadur,

#{constantsBean.constants.value}

should work. Your enum has a proper public getter for its value property. However, you should also make sure that you set the constants property of the managed bean to the desired enum value. You namely didn't do that in the code snippet posted so far and thus it remains null. EL does by design not print anything when a (base) property is null.

Here's how you could set it:

@ManagedBean
@ApplicationScoped
public final class ConstantsBean {
    private Constants constants = Constants.PAGE_LINKS;

    public Constants getConstants() {
        return constants;
    }
}

I'd however rename the property (and getter) to pageLinks for better self-documentability.

#{constantsBean.pageLinks.value}

---

An alternative is to use OmniFaces <o:importConstants>, based on your question history you're already familiar with OmniFaces and probably also already using it in your current project.

<o:importConstants type="com.example.Constants" />
...
#{Constants.PAGE_LINKS.value}

This way you don't need to wrap the thing in an application scoped bean.