Online change in Apple ID password as forgot old password. On my mac keeps asking me for old password. Although new password works through iCloud

Made online change of Apple ID password as forgot previous one. Change not reflected on my Mac. System preference on my Mac still asks for old password in order to set up new one. However, new Apple ID password works through Icloud. Have tried signing out of Icloud and then signing back in, in the hope for ID sync with Mac but Mac system pref still asks for old password in order to set up the new. Any advice??