You will have to manually enter your password (or copy/paste) just as you did the first time you entered the steemit website. Then your browser will give you the option to save your password for the steemitwallet.com site, which you then can do for future use.
Let me know if you have any further questions. You can find me on discord, telegram etc with the same name.
RE: Important Changes to Steemit.com and Wallet