Here's one method. Naturally, whoever runs it must have design permissions on
the BE database and tables. It also involves checking version levels (invented
by oneself) to see if an upgrade is necessary, though the routine also sees if
the upgrade has been done.
(Whenever you open the FE, check the version level between FE & BE, if the BE
needs upgrading then run the routine. This would be faster than unnecessarily
running the routine)
----------
(the style shows a bit of age, not looking for prizes :-)  )
----------
Public Function UpgradeTable(VerLevel As Single) As Integer
On Error GoTo Err_UpgradeTable

Dim db As Database
Dim dbs As Database
Dim td As TableDef
Dim MyField As Field
Dim i As Integer
Dim j As Integer
Dim s As String
Dim FullDBName As String

UpgradeTable = False

Set db = CurrentDb()
Set td = db.TableDefs("SomeTable")  'any linked table to find the BE
s = td.Connect
FullDBName = Right$(s, Len(s) - InStr(1, s, "="))

Set dbs = OpenDatabase(FullDBName)
'----------------------------------
'Check for extra NEWFIELD field
If VerLevel < 0.13 Then    'Whatever the version upgrade level is
   Set td = dbs.TableDefs("SomeTable")
   j = 0
   For i = 1 To td.Fields.Count - 1
       Set MyField = td.Fields(i)
       If MyField.Name = "NEWFIELD" Then
           j = 1
       End If
   Next
   If j = 0 Then
       Set MyField = td.CreateField("NEWFIELD", dbText)
       MyField.Size = 25
       td.Fields.Append MyField
   End If
End If
'----------------------------------
dbs.Close
UpgradeTable = True
Exit Function

Err_UpgradeTable:
   MsgBox Error$
   dbs.Close
   Exit Function

End Function
----------

The links in the frontend will update themselves
automatically the first time the table with the changes
is used.  Beware not to delete fields that are being used
in the frontend.  Doing this will cause the frontend to
have runtime errors.  There is no need to relink unless
you are changing the location of the backend on the
network or the links point to a data sources other than
Access.