To add this option to Outlook do the following:
Type Windows key + R to open the Run command then type regedit and press Enter.
Once open browse the the following directory in Regedit:
Outlook 2016
HKEY_CURRENT_USER\Software\Microsoft\office\16.0\outlook\preferences
Click on the preferences key, right click on it and choose New > DWORD.
Type or copy/paste showcontactfieldobsolete and press Enter.
Press Enter again to open it and set the value to 1
This will show the Contact linking field. Set it to 0 or delete the DWORD or to turn it off.
DWORD: showcontactfieldobsolete
Value = 1
Outlook 2013
HKEY_CURRENT_USER\Software\Microsoft\office\15.0\outlook\preferences
Click on the preferences key, right click on it and choose New > DWORD.
Type or copy/paste showcontactfieldobsolete and press Enter.
Press Enter again to open it and set the value to 1
This will show the Contact linking field. Set it to 0 or delete the DWORD or to turn it off.
DWORD: showcontactfieldobsolete
Value = 1
Open Outlook and open a new appointment, you should now see the Contact button enabled as shown above.
NOTE: Editing the registry can be dangerous as you could disrupt your entire operating system so tread carefully and at YOUR OWN RISK!