About three months ago I sent an email to ask a professor about postdoc position under her supervision. Her feedback on my cv was positive and she told me that she intend to apply for grant this year and consider me as a potential postdoc. She also mentioned that she keep me informed if the appîication for grant be successful. Indeed, she told me she will inform me, but because of the fact that professors are busy people, I do not know she remember me or not? I do not know whether I send another email to ask her about the status of availability of grant or not? If so, what should be a proper context of email to ask that.
It is perfectly reasonable for you to politely seek an update in these circumstances. She likely has not heard back about the grant, even if she submitted it the day that she emailed you (three months is not very long in a grant funding cycle), but she will have a clearer picture of what her plans are with regard to the application and, perhaps, with regards to you. It is a very busy time of year right now with the start of term (if she is in the northern hemisphere) so perhaps wait until the first week of October, but a short, to the point, and very polite email would be appropriate.
Definitely follow her and her team on the various digital networks that they may be on. Most teams have Twitter and university groups.
Figure out when the grant rounds are decided and published. Most national grants will have public websites etc. Private grant institutions may also have ways to follow them.
But what is more important for you is to know when your usual post doc dates and times are. Her grant may be after that time which may limit your choices. Keeping all the factors in mind is an important strategy.