I know someone in my program at Hopkins who has completed 3 years postdoc, her fellowship ended in June. But she is still around. Does that mean she is staying for another FULL year? (perhaps on a new fellowship) In other words:

Do postdoc positions, or academic outlets for postdocs, usually start at the beginning of the year (end august)? or perhaps semester? or it could be anytime within the year...?
Thank you

It is not uncommon in the UK for postdocs to start at any time of the year as far as I understand.
It is also not uncommon to find a PhD student or postdoc sticking around well beyond the end of their funding in order to keep their hand in.

I sense you are not telling us the whole story here. Is there a problem you have with this person and you are desperate to see the back of them?