If you want to use a Custom Form when creating a contact within a particular project, you must first assign that Custom Form to the project.
Steps
Go to the Project Preferences page
Search for the project in the top menu Search bar (or select My Apps > Projects)
On the project page, select More Options
Select Preferences
In the Contact Forms section, select the Custom Form(s) that you want to be available when creating a contact within this project
Press Save