Hide new button while saving a form

Hi is there a way to hide new button while saving a form button. Attaching two screenshots the one is while creating a new quote where the new button appears.

and second one is while saving the quote the new button appears. I want to hide the new button from this view any idea on how can I do this?

Are you saying you only want to allow a single child record? Or are you saying that the 2nd form is happening sometime later, while editing an existing record? Or something else?