It depends on who you mean by someone.
Another discord user will have no idea about your protonmail identity.
Similarly, a protonmail email recipient would have no idea about your discord identity.
Your phone would not reveal private info between the two apps.
There may be a possibility if both apps using push notifications using Google's FCM. I believe it should be anonymous. But Google might be able to glean some connection between the two.
If the someone is law enforcement with subpoena power in the jurisdictions hosting protonmail and discord server, then it's definitely possible. Protonmail will comply with lawful requests for information when activity that is a crime in Switzerland is being investigated. With that, it will be possible to identify IP addresses they have also accessed the discord server.