One day, an Office 365 user asked me why he cannot change his Teams Profile Picture. After a few check, we found that a license option was missing on his Office 365 user account. This user account was missing an Exchange Online license.
So, to enable picture adding to a Teams profile, you need to have an Exchange Online license enabled for this profile. Once it’s done, wait for un while or restart Teams and you will see the “Change picture” option appear.
To understand how Microst Teams interacts with Exchange Online, you can read the following complete Microsoft article https://docs.microsoft.com/en-us/MicrosoftTeams/exchange-teams-interact