Mail doesn't push

Push requires installing a token in the mail app that matches a token in the server. This only happens once when you set up the account, so something to try is to delete the account, restart your phone, and add the account back. Be sure you have a cellular connection and cellular data enabled when you do this.

If you care to know the details, see ➡️ If your Apple devices aren't getting Apple push notifications - Apple Support

And for incredible, overwhelming detail ⬇️ https://developer.apple.com/library/archive/documentation/NetworkingInternet/Conceptual/RemoteNotificationsPG/APNSOverview.html

You may know that there are two settings (Fetch and Push Mails). What have you set? Watch the GIF below

Google, AOL, Yahoo - Only Fetch mail Option is available

iCloud, Exchange, Outlook - Both Fetch and Push Mail option is available

1. Push Mail: Whenever possible the email client will push mails to all your devices.
2. Fetch Mail: You need to set How you want it to be fetched, Automatically, Manually , Hourly,Every 30 mins, every 15 mins
   1. Automatically: will fetch when the iPhone is powered and on WiFi
   2. Manually: with fetch when you open email, open Inbox and swipe down
   3. You get an email notification as soon as the client server receives an email and your device is connected to internet, irrespective of whether the mail is in your device's Inbox or not

Make sure that you entered the account correctly as an Exchange account and activated Push. If that does not work, you need to contact your Exchange administrator at work and have them help you troubleshoot this. There has to be a connection issue between your account and your phone, and only the Exchange administrator can troubleshoot that.

SravanKrA is a volunteer user, like everyone who posts in this user-to-user forum. As he is extremely active (on the list page look at the bottom to see how often users mark his posts as Solved or Helpful), in order to keep up he has a library of responses. This is one of them. As you didn’t say that you know what Push is and he isn’t a mind reader he probably thought it was worth explaining the various mail retrieval options.

Push should work with Exchange, but you may need to have cellular connection for it to work.

I'm sorry, but if the account was working fine, you would be receiving your mail via Push. Since you indicate your mail is not working correctly, you need assistance from your Exchange Administrator. They determine how it goes out to your iPhone. They control all of that from their mail server. Talk to them.

Check to make sure your administrator does not have restrictions for the number of devices you can have set for your account. Even if it works fine with other employees, the admin needs to check the connection for your particular device.