How can I make my phone require a password to open Google Play Store?

You can try AppLock.

On its Play Store page, it is stated that:

AppLock can lock Facebook, Whatsapp, Gallery, Messenger, Snapchat, Instagram, SMS, Contacts, Gmail, Settings, incoming calls and any app you choose. Prevent unauthorized access and guard privacy. Ensure security.

Below are the steps to configure the app:

1. Install the app. After the installation is completed, open it.



2. You will be prompted to create a pattern that will be used to unlock the app (I advise you use a different pattern than the one used to unlock your phone).

   
   
   

   




3. The next windows will ask to enter an email address for security purpose.

   
   
   

   




4. Next, a dialog box will appear asking to grant the app usage access. Click permit, then on the list select APPLock and switch on usage access permission.

   
   
   

   




5. Go back to the app, click on the Play Store. It will now be locked.

   
   
   

   




6. When you or anyone else try to open the Play Store, he/she be prompted to enter the pattern you created.

   
   
   

   

Disclaimer: I have no relation with those who develop the app.