You will probably want to set the default address book in your Outlook to the GMail Global Address List.
To do this
1. Ensure you have Outlook open and go to the Contacts tab in the bottom left. It's the icon with two people.
2. Once in Contacts, click Address Book in the top right
3. Click on Tools then Options
4. At the bottom, change When opening the address book, show this address list first: to Global Address Book
5. Click OK and then close the Address Book. Switching back to mail in the bottom left (envelope icon).
Now when you compose a new email and click To or Check Names it'll default to the Global Address List.