My honest opinion is that you do not need Kaspersky browser extension. Other extensions like Adguard do the job better (block tracking and ads) and you have Kaspersky web detection still running in the background. Anyway I'm not the right person to help you if you really want to get back the extension in that situation.
Try searching the Google Chrome store or the Kaspersky interface for a way to get it, if not then check the installation path and let me know if you can find the *.crx extension file (if you can then you can manually install it ). if not then try reinstalling kaspersky and that should do the trick
Without KP and the injected script some modules/features can be affected: Safe Money, Private Browsing, Secure Data Input, URL Advisor, Anti-Banner, Parental Control...