It sounds like maybe you need to become familiar with "MS Access Linked Table Manager" and, perhaps "MS Access runtime." You should easily be able to "continuously deliver" once you figure just a couple things out, i.e., how to deploy. Multiple options most with minimal or zero code. It does require research, investigation and testing for your specific, optimal solution. No doubt consider splitting your solution into two (2) files a: 1.) front-end; and, 2.) back-end.
There are more solutions for this, I will tell you mine
As mentioned it is wise to split database and frontend. Access provides a function for this.
For updates you are stuck with the old database because the customer is using the data and adds and updates it a lot.
You can write a procedure (or let it be writen for you) what is checking if the frontend is new, makes a backup of the current database containing the data, alters the tables as desired in the current database based on a database you provide/include with the update, updates values as needed and add records to tables what you need (for example settings stored in tables).
The same goes for the reports, forms, modules etc. You can even design it that it will remains safe. So the end product is a executable database compiled so nobody steels your code.