I know that in German, unlike English, Verspätung (delay) is a quantifiable noun, meaning that the following sentence is grammatically incorrect: "Der Zug hat eine Verspätung" Instead, the following must be said: "Der Zug hat Verspätung".
I was wondering whether this is also the case in the following example. "Es gibt Verspätung"/"Es gibt eine Verspätung" What is the correct sentence? The one with the indefinite article (eine) or the one without it?
My interpretation is that "Verspätung haben" is one of a number of fixed phrases involving "haben". Some others are "recht haben" = "to be correct", "zu tun haben" = "to be busy", "Hunger haben" = "to be hungry", "es eilig haben" = "to be in a hurry", "lieb haben" = "to love" and "Angst haben" = "to be afraid". This makes "haben" a light verb in these phrases, meaning that the verb itself has little meaning in itself, but combines with another word to produce a related meaning. German has other light verbs: "Hilfe leisten", "Spaß machen", "eine Wahl treffen"; and English also has light verbs: "take a shower", "give a hug", "have lunch". It's best to think of such constructions as fixed phrases and to not read too much into the grammar and the meanings of the words individually. (By doing so you can turn them into jokes: "I took a shower./Where did put it?" "Will you give me a hug?/Only if you give it back." I don't know if such jokes are possible in German.) So "eine Verspätung" is certainly possible: "Wir erwarten eine Verspätung." But it doesn't belong in that particular fixed phrase; fixed phrases generally don't allow changes even if they make sense grammatically. Even in a fixed phrase, modified nouns are more likely to use an article in German, so you can say "Der Zug hat eine viertel Stunde Verspätung."
The conclusion is that you can't infer from "Der Zug hat Verspätung" whether a article is needed with "es gibt" or not. In fact "Es gab eine Verspätung" would be the expected way of saying "There was a delay."
Der Zug hat Verspätung
is an example for Nullartikel, subsection Abstrakta: you will not qualify the delay further, but just point out, that in-time does not apply. This is similar to The train is delayed.
As soon as you add additional information, the indefinite article again becomes necessary as in
Der Zug hat aktuell eine Verspätung von 12 Minuten.
Another variant of the statement would be:
Der Zug hat aktuell 12 Minuten Verspätung
This is another condition triggering the Nullartikel, since it is a measurement specification, similar to 300 g Butter, with Butter taking the role of involved substance (Verspätung in your example).
A sentence according to the same pattern as your example is:
Seine Aussage hat Gewicht.
(His statement is of importance.) You can't quantify the importance (or in literal German meaning the weight, where the corresponding unit kilograms is obvious nonsense.)
The example from your question title quite urgently requires additional clarification, since without context es gibt most often means exists; it is obvious that delays happen, so a rephrase, is recommended.
Both examples rather sound unusual, you would rather say "Der Zug hat Verspätung", but it definitely sounds better without the article.
"Der Zug hat eine Verspätung" is definitively the usual expression to say that a particular train is delayed.
I'd read "Es gibt Verspätung" as a more general and slightly colloquial statement about a delay that is expected for sure but which is not yet actual. More usual would be plural "Es gibt Verspätungen [auf der Strecke A - B]" (delays are expected).
(DB would be less colloquial and say: "auf der Strecke A - B kommt es zu Verspätungen")
