Hi @Pierre Landau ,
As I know, Outlook for IOS actually could support Exchange 2013 account, but according to your description, your account could work normally on other client except the Outlook for IOS, so this issue may be related to the Outlook for IOS itself. As a workarouond, please try to remove your account and add it again, or you could directly uninstall and reinstall your APP to check if the issue has any difference.
If the issue still exists, due to here we focus on general issues about Outlook Desktop Client and we may know little about Outlook for IOS, it's suggested to post a new thread in this forum:
https://answers.microsoft.com/en-us/msoffice/forum/msoffice_outlook-mso_imobile?sort=LastReplyDate&dir=Desc&tab=All&status=all&mod=&modAge=&advFil=&postedAfter=&postedBefore=&threadType=All&isFilterExpanded=false&page=1
The reason why we recommend posting appropriately is you will get the most qualified pool of respondents, and other partners who read the forums regularly can either share their knowledge or learn from your interaction with us. Thanks for your understanding and hope your question will be resolved soon.
If the response is helpful, please click "Accept Answer" and upvote it.
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.