Where exactly are you placing the code you posted?

code that verifies required fields needs to be placed in the before update
event of the form.

code that moves to a new record, or adds a new record simply needs to be
placed behind a button, or whatever you plan/are using.

Using the "standard" navigation buttons will even suffice. (or you own!!).
Either way, if the user moves to a new record, and does not enter any data,
then trying to move to another new record WILL NOT OCCUR.

So, put your field verification code in the before update event (and note
how it has a cancel event).

Right now you have code that is just going to tie you up in knots..and are
making this really difficult. Further, the user might not try and move to a
new record, but close the form..and you STILL want to verify those fields.

Step back here for a second...

There is no need to use me.NewRecord here. You mean I can go and erase the
supplier name in a existing record (not a new one), then hit the add a
record button, and yet the supplier name is now blank? (this is not good).

The trick to making this all work as smooth as glass is to use the correct
events in the form, and when you do, this will all work, and work with a min
of code.

Note that the code in the before update event DOES NOT RUN if you don't
modify the record!

And, if you don't modify the record..then it does not need to be saved....

So, lets first build our add new record button. You simply need:

 DoCmd.GoToRecord , , acNewRec

The above is ONE line of code. If the user hits the button more then once,
access will NOT navigate to a new record. So, this solves the duplication,
or simply prevents the user from be able to add a whole bunch of blank
records. Ok??? One of code!!! Further, our code that checks for required
fields (in the before update event) will CANCEL the move to the new record
for us if there is any problem (and, in fact will cancel a form close...and
a zillion other events that can occur that will want to SAVE the current
record. (you can't write your check code in 20 places....so, put it in the
before update event).

Note that you can set the required fields in the table design view, and not
have to write any code.

However, in most cases, writing some code to "verify" the input is a good
idea, an gives the user a nice message.

As mentioned, the before update event is what we want. Here what the code
could look like:

If IsNull(Me.[SupplierName])  = true Then
  cancel = true
  msgbox "suppler name is required",vbExclamation,"required"
  me.SupplierName.SetFocus
  exit sub
end if

So, if a person navigates to a new record, and does nothing..then the blank
record will be discarded.

If the person edits this new record, and changes their mind, then they must
either go edit->undo, or you provide a "delete" button.? (how are planning
to train, or give users the option to delete a record they accidentally
added? - how do they do this now???).