I would say Singleness/Being single late in life.

Spinsterhood...?

Self-partnered is a new interesting term. theconversation.com/…

spinster: en.wikipedia.org/wiki/Spinster

Is there a gender-neutral term, apart from 'unmarried oldie'?

You will need to be careful about the tone. Do you want a term that is neutral? Or that implies the person is somehow a failure because they never married? Or even that they are somehow superior because they are unmarried?

Both answers are heavy with connotation, and binary. Either, divorced or [un- / never] married.

@BobaFit completely neutral, non judgemental in any way...

Out of curiosity – what was the original word you were trying to translate?

@MCEmperor the article was in Hebrew, and the word was "רווקות מאוחרת" which in Google Translate is translated to "Late bachelorhood"

Freedom? (or is that too cynical against the institute of marriage?)

@Michael What are the nuances of that Hebrew term that you want in the English term? Is it slightly pejorative? Is it part of the term that they are interested (or not at all interested) in making a relationship? Does the age have to be -in- the phrasing, or simply implied eg "woman of a certain age"? etc etc. What is the context in the original? Is the phrasing in Hebrew a new term there for a new sociological phenomenon? Is the phrase simply descriptive? So many nuances..please add to your question.

@Mitch At the risk of stating the obvious "single" is not the same as "seeking a relationship".

The question, as formulated, includes those who are divorced and widowed, and yet most of the comments and answers focus on those who have never been married, A clarification is needed about what was intended.

@DJClayworth Yes, that is obvious to an English speaker, but may not be an obvious implication (given their terms) to someone who needs a translation. Those were only examples. The OP needs to give all the nuances (even the obvious ones).

This question seems to me off-topic, in that it has no explanation of the context in which such a term would be needed. There is, sadly, nothing unusual about the phenomenon of lone old women, for the simple reason that women on average live longer than men. You need to explain why this characteristic is of interest. Such a classification could be regarded as offensive. Describing women as 'spinsters' (or men, for that matter, as bachelors) is widely and rightly frowned on. I see that you have accepted the word 'spinster'.

@Michael Please see our help for single-word-request questions and our help for translation questions. Currently this question does not match the criteria for either tag.