So new cases went up to an average of 31 per day at its peak July 22nd, then dropped back down and continue to drop. This was a small, temporary increase.
Now, the obvious question is "why did it go up at all?". Well, first not everyone is eligible and about 20% of those new cases are among unvaccinated people (mostly younger people). Are those cases serious? Almost certainly not. But they add to the total just the same. For those vaccinated, there are a couple issues which can present. First, anyone who's immuno-compromised (e.g. cancer patients, organ recipients, people with autoimmune disorders, the elderly) are often unable to effectively fight infections regardless of vaccination; they don't have enough of a functioning immune system for it to immediately wipe out anything significant.
Second, the Delta variant has mutations in the N, M, and S proteins. These mutations change the structure (folds) of the proteins such that antibodies created for previous variants don't fit as neatly into place anymore. This means more antibodies need to hit before one can "click" into place to neutralize that particular protein on the virus surface. The more significant those structural changes are, the less likely existing antibodies will neutralize all the surface proteins before the virus can infect a cell.
The important thing to note here is this: prior to their vaccination campaign, Gibraltar racked up one of the highest COVID-19 deaths per 1 million population in the world at 2,821. The population of Gibraltar does NOT do well with COVID-19 infections. They seem to experience far more problems than most with it. Since their mass vaccination campaign, they have had 1 death from COVID. Just 1 COVID-19 death since the middle of March. That makes them one of the least impacted places in the world.
In other words, before vaccination, they were dropping like flies due to COVID-19. After mass vaccinations, they have seen a small number of cases and virtually no deaths. That's a massive turnaround.