Is the only way to update password stored in Keychain, to delete the old/existing stored password & re-add its new “update”

You can work around this using the 3rd party macro/scripting app called "Keyboard Maestro", from http://www.keyboardmaestro.com

Here's a screen shot of the simple script I use. Currently it only works when the App Store is in the background, and gets automatically activated by clicking a web link in Firefox or something, but you get the idea, this could be modified and improved in various ways.

Needless to say, security is compromised by storing your password in plain-text within Keyboard Maestro script, so be sure it's a unique, random password that you don't use anywhere else.

If you change your account's password using your Mac OS X Install disc (or if your network-based account password is changed due to a network admin forcing a password change), your default keychain password (which uses the same initial password as your user account) does not change.

Support Apple helps:

If you want your default keychain to be unlocked automatically when you log in, synchronize your Keychain Access and account login passwords by doing this:

1. Open Keychain Access (you can get to it by choosing Utilities from the Go menu in the Finder).
2. From the Edit menu, choose Change Password for Keychain "login."
3. Type the former password of the account that you are currently logged in to, then click OK.
4. If you entered the correct password, a new window appears; enter the original password again in the Current Password field.
5. In the New Password field, type the password that matches your current account password.
6. Re-enter the newer password in the Verify field, then click OK.

If you don't remember your original (former) account password

If you don't remember your original password, you'll need to delete the keychain. Deleting a keychain also deletes all the password data saved in that keychain.

1. In Keychain Access.app, choose Preferences from the Keychain Access menu.
2. If available, click the Reset My Default Keychain button. This will remove the login keychain and create a new one with the password provided.
3. If Reset My Default Keychain is not available, choose Keychain List from the Edit menu.
4. Delete the "login" keychain.

The next time you log in to the account, you can save your current password in a keychain.

If the above fails or doesn't fit:

1. Open Keychain Access.app
2. Select the "login" keychain from the keychains list
3. Click the lock at the top to lock the "login" keychain
4. Click the lock again to unlock the login
5. After entering your "login" keychain password you should be presented with a dialog
6. Clicking the reset button will re-sync your "login" keychain password with the iCloud keychain password.

Info: Discussions Apple

If everything from the above fails for whatever reason the last resort you can do is the following:

1. Quit all running Applications
2. In Finder Select Go > Go to folder (⇧⌘G)
3. In the window that appears, type the following: ~/Library/Keychains/
4. Click OK.
5. Look for a folder with a random name similar to this "A8F5E7B8-CEC1-4479-A7DF-F23CB076C8B8". Note: Each folder has a unique number.
6. Move this folder to the Trash.
7. Immediately choose Apple Menu () > Restart… to restart your Mac.

Info: Support Apple