I am still waiting to get an answer from my prospective Ph.D. supervisor. On July 15, 2019, I have sent my master transcript and initial statement of research upon his request, and a week after I sent him another e-mail in a very polite manner to make sure that he could open my file without difficulty, but there was no reply. As the university located in New Zealand I am sure they are not in the mid-semester break, I told them that I am going to apply for July 2020, I do not know what to do now. Should I dismiss this case and go for another supervisor, or send him another email to see what is going on? or should wait a little bit longer? At first, he showed his eagerness and told me that he had to talked to his colleagues about my research proposal and interest and then let me know about the outcome. Thank you guys for your answer.
Academics tend to get a ton of email, and their attention tends to be split lots of different ways. My guess is that the supervisor plans to read your email carefully and then reply, and hasn't done so yet. Alternatively, the outcome might depend on external factors (e.g. availability of funding), and the professor might be waiting on that.
If the application deadline is soon, or for some other reason you need a reply soon, then you could send an email asking about the status. Otherwise, I would recommend waiting a bit longer.
Remember your prospective supervisor is only human, with their own personal life, obligations, and work load. Semester 2 started in New Zealand around 22 July and I imagine it is a very busy time for whoever you contacted. They likely have a very full inbox.
It's been long enough for a polite email asking if they saw your previous message and if they would like any further information from you.