Make sure that the other email app is installed. Although you might be able to use a web browser for email (webmail), a web browser isn't an email app. Open the Mail app.

Choose Mail > Preferences, then click General.

Choose an email app from the ”Default email reader” menu.

You might be prompted to add an email account before you can change the setting in Mail. If you don't want to do that, check the preferences of the other email app. You might be able to set a default email app from there.