Let's first be clear that I've understood correctly what you want.  The way I
read your original post was that for each initiation year and each parent
type you wanted to number the rows sequentially starting with 1, so the table
might look like this:

InitiationYear    ParentType    ID
------------------------------------------
2007                  Foo                 1
2007                  Bar                 1
2007                  Foo                 2
2007                  Foo                 3
2007                  Bar                 2
2008                  Foo                 1
2008                  Foo                 2
2008                  Bar                 1
2008                  Foo                 3
2008                  Bar                 2

Is that what's wanted?  The code is right for this, apart from the fact that
you've missed the 'And' operator out when building the string for the
criteria to look up the highest existing value.  It should be:

Private Sub InitiationYear_AfterUpdate()
Dim strCriteria As String
If Not IsNull(Me.ParentType) Then
   strCriteria = [ParentType] = """ & Me.ParentType & """ & _
       " And InitiationYear = " & Me.InitiationYear
   Me.ID = Nz(DMax("[ID]", "Table1", strCriteria), 0) + 1
End If
End Sub

Private Sub ParentType_AfterUpdate()
If Not IsNull(Me.InitiationYear) Then
   strCriteria = [ParentType] = """ & Me.ParentType & """ & _
       " And InitiationYear = " & Me.InitiationYear
Me.ID = Nz(DMax("[ID]", "Table1", strCriteria), 0) + 1
End If
End Sub

The way it works is like this:

If we take my dummy table above and you enter a new record with 2008 as the
initiation Year and Foo as the type the string built as the criteria would be:

ParentType = "Foo" And InitiationYear = 2008

The DMax function looks for the row in the table with the highest (Max) ID
value where these criteria are met, i.e. the parent type is Foo and the
initiation year is 2008.  This value is 3, so by adding 1 to this we come up
with 4 as the value for the ID in the new row being added.  The Nz function
is used because if there are not yet any rows which meet the criterion then
the DMax function will return a Null.  The Nz function converts this to a
zero, so adding 1 to this gives us 1 for the ID.

Where you say "I'm wondering if that concatenated value can be added to a
DIFFERENT table for later use?" I'm not sure what you have in mind here?  I
think you are probably thinking of how to relate another table to this one.  
If so then, as the InitiationYear, ParentType and ID make up a composite
primary key for this table, you can repeat the same three columns in a table
related to it, so that they form a composite foreign key in the 'referencing'
table.  You'd probably use a subform for data entry into this table so the
values from the 'parent' record would automatically be entered into the three
columns in the 'child' records related to it.

An alternative would be to add an autonumber column to the current table to
act as its primary key and a corresponding long integer number column in the
'referencing' table as a foreign key, but not an autonumber in that case.  If
you do use an autonumber column as a 'surrogate' key instead of the composite
'natural' key of the three columns in the current table its important that
you create a unique index on the three columns in the current table (that's a
single unique index on all three, not separate indices on each) to prevent
invalid duplicate data being entered.  If you do define all three columns as
the primary key then this automatically creates a unique index.

Ken Sheridan
Stafford, England