No, Kaspersky Password Manager does not have any account recovery options. If you forget your master password, you’ll have to create a new vault entirely.
If you’re looking for a password manager with good account recovery options, I recommend LastPass. LastPass has strong security and more account recovery options than any other password manager — including mobile account recovery, one-time recovery password, SMS recovery, and more. It also comes with an emergency access feature, which lets you assign an emergency contact to recover the data in your vault if you can’t access it.