Hello Barry,
Did you configure your Office 365 account in Outlook and tried to migrate your old ost file to Office 365?
Please refer these steps and check if the old ost emails can be moved to your mailbox on Office 365 successfully:
1. Open Outlook with your old ost file and check if you are able to access emails from that old ost.
2. Add a new Office 365 account into Outlook.
PS: Please make sure you don’t modify settings of the old account.
Configure E-Mail in Outlook 2010
3. Copy emails from Inbox of your old email account to folders under Office 365 mailbox from Outlook.
4. Wait till these emails are synchronized back to Exchange Online.
5. Remove your old email account from Outlook.
I hope this solution will easily import OST to Office 365 account.
Thank you
Eddie