you need to handle the AfterUpdate in both Employee_ID and SkillName. Something like
Private Sub Employee_ID_AfterUpdate()
UpdateEmp_Skill_ID
End Sub
Private Sub SkillName_AfterUpdate()
UpdateEmp_Skill_ID
End Sub
Private Sub UpdateEmp_Skill_ID
If Not IsNull(Employee_ID) And Not IsNull(SkillName) Then
Emp_Skill_ID = Employee_ID & "_" & SkillName
End If
End Sub