I have the same phone and also use Gmail. I do get a very gentle tap when I receive an email, and a popup at the top of the screen, and a notification in the task bar. The sound is rather subtle but still quite noticeable. I can't find where to change the sound. I didn't change anything to get it working. I do know a few settings that might be connected to your problem, so just to make sure the obvious stuff is set correctly:
In System settings - Notifications, there should be a listing of all apps that are allowed to notify you. For me that's External drives, System Settings, Facebook, Gmail and Telegram. To the right of each entry is a radio button to switch it on or off.
So: is Gmail listed there? If so, and turned off, easy fix. If not, your account may not be OK. Go back to system settings and to Accounts (one to the left). There, Google should be listed with your mail address underneath. If so, enter it by tapping. At the top is your ID, below are the different apps that use Google account. Is Gmail shown? Is the button switched on?
If you're in doubt whether your account settings are correct, you could remove and add back your google account from the accounts settings.
Otherwise, I wouldn't know what to do... Good luck anyway!