Biodiversity Hotspots should work, but almost everyone adds the condition that the area is threatened and must be preserved. What about relatively high species rich areas that are protected already and not in imminent threat
I understand your reservations about the term "biodiversity hotspot". However, technically and strictly speaking, the term is not normative in its narrower sense and thus signifies exactly what you mean - a geographical unit/area (of whatever size) featuring, in relative terms, a particularly high degree of biodiversity. However, as you know, the term "biodiversity" itself is rather vague and therefore should be specified in each case in my opinion --> e.g., floral/faunal diversity, diversity of specific taxa etc. There are various ways to measure it. So I would usually use phrases such as "The overall floral diversity of area x (i.e., total number of all floral species/genera/families...) is particularly high relative to/within the surrounding areas y and z". Wordings such as "extremely diverse in taxon a", "very high rates of diversity in taxon b" will also do - but always state in relation to what other spatial unit(s) you deem the area at hand as particularly biodiverse! Specific other indicators such as rate/number of endemic species etc. may be added, too.
Personally, I would use the "hotspot" terminology only in cases of outstanding or extreme relative biodiversity (on whatever given scale: local, regional, global...). If you follow a more quantitative approach (think, e.g., of a "biodiversity landscape" plotted on a 3D or 4D diagram), you may also use terms such as "area of absolute/relative biodiversity maximum/minimum /peak/trough...".
You’re right that the term biodiversity hotspot is often used with the added connotation of threat and urgent conservation need, so it may feel misleading when describing already protected or stable areas. In such cases, many researchers simply describe them as species-rich areas, centers of diversity, or areas of high biodiversity, and then clarify the taxonomic group or scale of comparison (e.g., “this forest patch shows particularly high odonate richness relative to surrounding landscapes”). If the diversity is especially striking, some still use hotspot in its strict, non-normative sense, but it’s usually best to frame it more neutrally and quantitatively, pointing out whether it’s floral, faunal, endemic, or overall richness, and always relative to other areas. This way, the description captures the ecological reality without implying a conservation urgency that may not apply.