It seems you are trying to edit your colleague's events. If you want to do this, you need to have an additional right from the roles side to do this. You need to contact your Teamgate account admin and ask them to follow these steps:
1. Navigate to Settings > Users management > Permissions & Roles and select the role you want to edit.
2. Select Organizer and mark the Edit and Delete other activities.
3. Don't forget to save your changes.
After your settings are saved, you will be able to edit not only your but your colleague's events too.
Note: Use this feature carefully, because you can edit another person's events and delete them permanently. If you don't really need this feature and having the view-only mode is enough for you, don't give this right to others.