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From what I know, the latest season of 'Highschool DxD' (Season 4) ended a while back and currently, there are no concrete announcements of a new one. That being said, light novels of the series are still ongoing. So to answer your question, the anime adaptation may or may not be over but the series as a whole isn't.
Last I checked, 'Highschool DxD' ended with its fourth season. There hasn't been any word on a fifth season yet but the light novels continue. So, while the anime may seemingly be at a halt for now, the series lives on in the novels.
'Highschool DxD''s anime adaptation concluded with its fourth season, and and at the moment there's no official information about any upcoming seasons. But don't be too disheartened! The light novels continue to further the storyline. So, although the anime might be over, the story is far from done.
As an anime, 'Highschool DxD' currently stands concluded after its fourth season. No news of a fifth season yet. However, for all you hard-core fans, the series is very much alive in the form of light novels. Conclusion? The anime may be finished for now, but the series? It persists.
'Highschool DxD''s anime counterpart had its run till season four, after which there haven't been any immediate plans for a fresh season. But worry not, because the series still continues in the form of light novels. Therefore, the anime may have reached a stop-point, but the larger series continues!