To add contact onto an Account customer quote is easy. First you need to make sure you have the contact in the system. Learn how to do that here.
You also need to up date your quote template with the relevant contact placeholders
Now that your Template is updated.
To add your contact on to the quote, Follow these steps
There is a new box that will appear called contact under the Account customer's details
If its an old contact you can check or edit the details to make sure they are still correct
Continue your quote as normal.