1. Open Outlook ( choose the new Office 365 profile in the prompt to select the profile )
2. Go to File ---> Import and Export ("Open" for Outlook 2010) ---> Import from another program or file ---> Outlook Data file ---> Browse your PST file(calendar or contacts PST file) and select do not import duplicates ---> Click on your name/data file (root folder, as shown in the image below, or any folder in the PST file that you wish to import) and check Include subfolders. Also select the new mailbox to which you want to import from the dropdown under "Import items into the same folder in:" ---> Click Finish.
Browse the contacts or Calendar PST file ( You will need to repeat these steps twice for both the calendar and the contacts PST file that you exported from your old profile ) :
Select the calendar file as shown below and click finish (it will take some time after you click finish):