I sent an informal query to a professor in UK and she replied me with her strong interest in my research works and considering me as a potential postdoc. She mentioned that she wants to apply for research grant this year and will inform me when she gets that. But she did not provide some details on the approximate time which she probably get the grant. In the meanwhile, I am a postdoc in another country and my contract will be finished within 4 months. As I need to make some plan about renewing my contract, is it appropriate to ask her to let me know about the approximate time of approving her application for grant? As a note, one of her postdocs has resigned but the remaining time of the current project is rather short. Can I make a request to join her team for recent project as well and wait to confirm her new grant in the meanwhile?
Don't be intimidated that she is a professor. It is certainly appropriate to continue your "conversation". Let her know of your interest in joining her team (possibly subject to funding) and give any constraints you might have. You don't need to say a lot, but thank her for her interest and express yours.
Ask her for any advice about what you can do at the current time if it seems like there is a possibility to work together.
In other words, write as if you are a colleague, not a subordinate.