My site is already mobile/tablet responsive. If we install AMP, what will happen to the existing mobile/tablet responsive pages

Your existing mobile/tablet responsive pages will remain. The AMP pages utilize their own theme, and this theme works separately from your mobile theme.

The AMP theme will be working for the customers that came to your website from the Google AMP search results page. In other cases, if customers come to your website directly - your regular mobile theme will be displayed.

However, with Plumrocket AMP Plugin, you can also force all mobile users to view only AMP theme if option "Force AMP on All Mobile/Tablet Devices" is enabled in module configuration.