My suggestion (collect others' ideas, too) would be to use something else
(?an Autonumber field) as a primary key, and use a query to concatenate the
YYMM### for user consumption.  Don't have them working directly in the
tables, but in forms (and reports) instead.

Regards

Jeff Boyce
Microsoft Office/Access MVP

Maybe try something like this.  This uses two separate fields as a primary key.
This will probably only work with a single user database. I have read that
self-baked numbering sequences always fail in a multi-user database.

Copy sub code to a module of a new database and type
call CreateFeedings in the immediate window.
(not really tested)

Sub CreateFeedings()
   With CurrentProject.Connection
     .Execute _
     "CREATE TABLE Animals" & _
     " (animal_nbr INTEGER NOT NULL" & _
     ", animal_name VARCHAR (25) NOT NULL" & _
     ", PRIMARY KEY (animal_nbr));"
     
     .Execute _
     "CREATE TABLE Feedings" & _
     " (intake_date DATETIME DEFAULT Now() NOT NULL" & _
     ", intake_sequence INTEGER DEFAULT 0 NOT NULL" & _
     ", animal_nbr INTEGER DEFAULT 1 NOT NULL" & _
     ", CONSTRAINT FK_Animals" & _
     " FOREIGN KEY(animal_nbr)" & _
     " REFERENCES Animals(animal_nbr)" & _
     ", CONSTRAINT PK_Feedings" & _
     " PRIMARY KEY (intake_date,intake_sequence));"
  End With
End Sub

form: frmFeedings
    txtIntakeDate
       txtIntakeSequence enabled and locked
       txtAnimalNbr

Private Sub txtIntakeSequence_GotFocus()
  If Me.NewRecord Then
     Me.txtIntakeSequence = Nz(DMax("intake_sequence", _
     "Feedings", "DateDiff('m',0, #" & Me.txtIntakeDate & "#)" & _
     " = Datediff('m',0,intake_date)")) + 1
  End If
End Sub