Let's say that the field size is 10. The input mask would be:

 0000######

That makes the first four digits mandatory and the last 6 digits optional.
If any of the last 6 aren't entered, they are NOT stored as spaces.

   Are you using a text field or a number field.  Tables do not same
numbers with leading zeros.  You can display numbers with leading zeros as a
format in queries(?), reports and forms.  If you choose text then you will
not be able to do math computations on the text.

Hi Una

I would not bother with a mask.  -  Up to you though.

If you are using a form to update the record I would use the AfterUpdate
event of the control to alter the data.  Something like this

Private Sub FieldName_AfterUpdate()
If Len(Me.FieldName) < 5 Then
Me!FieldName = Right("0000" & Me!FieldName, 4)
End If
End Sub

Change "FieldName" to what it is on the form and it should be OK.

If the data is "always" 4 digits you could set this as a variable and use
something like this

Private Sub FieldName_AfterUpdate()
Dim SomeName As Long
If SomeName = Len("FieldName") < 4 Then
Me!FieldName = Right("0000" & Me!FieldName, 4)
End If
End Sub

Change FieldName again and I wouldn't use "SomeName" so change this as well.
Note this will of course trim the data to 4  so don't use if this is not
what you want (not really sure from your post).  Or include an "else" to the
above to show longer strings.

Hope this helps