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The purpose of hashing a password is to irreversibly hide the original password. Password hashes are stored in a database instead of cleartext password, so that in the event that the database has been compromised by hackers, they will not know the original passwords. This means they might know the usernames, but they will not be able to access those accounts (at least not without investing resources to crack those hashes).
Back to your problem, if you store password hashes, and you want users to submit password hashes, then it defeats the whole purpose since the password hashes will then effectively serve as the cleartext passwords as well.
To answer your question, yes, it is safe to POST cleartext passwords if password hashes are stored in the database. If you want to improve security, use HTTPS so that the cleartext password is encrypted in transit to the server.
EDIT :
To clarify, when I said:
it is safe to POST cleartext passwords if password hashes are stored
in the database
I mean it is safe from the attack vector specified in the example above (hackers compromising the database to take control of accounts).