Hi Amy and Jochen Thank you so much for your quick reply

Following is my answers are in BLUE

1.  Is the field "Computed when composed", Editable, or Computed? 

Field is computed

2.  Do you have multiple values listed in the programmer's pane, as allowable readers?   
*if so, the values need to be separated by a colon ( : ) 

Yes and they are listed like this in the Field "[Admin]":"[Reader]"

3.  Are the users with this role listed individually in the ACL, or as a member of a group, Or both? 
*A user listed individually takes precedence over a group.  So if a user is in a group with Author access WITH role AND listed individually as Author WITHOUT role, the user cannot see the docs because their individual listing wins over the group listing. 

They are listed individually 

4.  Could the role be called "Leaders" instead of [Leader], or some other variation that may be slightly different between the readers field formula and the role name itself? 

Yes

5.  What steps did you use?  Is it different from the steps I outlined below?  If so, please explain. 

Database is already in use and has thousands of documents. There are 4 Fields:

2 Readers Type Fields as follows:

1) Field name is = Readers (Editable, contains individual names)

2) Field name is = HiddenSec_1 (Computed, contains "[Admin]":"[Reader]")

2 Authors Type Fields as follows:

1) Field name is = Authors (Editable, contains individual names)

2) Field name is = HiddenSec (Computed, contains "[Admin]":"[Author]")

ACL Default is NO ACCESS

'Enforce a consistent ACL...' is enabled on the ACL's 'Advanced' tab

Yes and it is being used from the Local replica

Recently I added a new user to the database who should see all the documents. I gave him the Role "[Admin]" in order to see all the documents and also created a new Role called "[Leader]" since "[Leader]" Role is not yet added to the documents I thought he should see all the documents because "[Admin]" is already there.