In the Close event:
   Forms!ParentFormName!SubformName.Form!ComboBoxName.Requery

Replace my placeholders with the appropriate names.

I would also use Richard's IsLoaded function to make sure the Parent Form is loaded.

Is Form Loaded

Kevin nailed it, as always.

Put the Requery in the Close event of your Contact form, since that is the point where the new contact has been saved and the user is returning to the Project form. Or I personally prefer to make a close button and turn off the close box. That way, you control exactly what happens. I do the same thing with delete.

Just be sure you are referencing the subform control name, which is not always the same as the name of the form object loaded inside it. The general syntax is:

Forms!ProjectF!ProjectContactSubformControl.Form!ContactCombo.Requery

And yes, using IsLoaded first is a good safeguard if the Contact form might ever be opened from someplace other than the Project form.