I figured it out! Basically you have to repeat the bold part twice in the code, one for each pivot table:

Private Sub Worksheet_SelectionChange(ByVal Target As Range)
 
'This line stops the worksheet updating on every change, it only updates when cell
'A1:B2 is touched
If Intersect(Target, Range("A1:B2")) Is Nothing Then Exit Sub
 
'Set the Variables to be used
Dim pt As PivotTable
Dim Field As PivotField
Dim NewCat As String
 
'Here you amend to suit your data for first pivot table
Set pt = Worksheets("New Business").PivotTables("PivotTable7")
Set Field = pt.PivotFields("Job No.")
NewCat = Worksheets("New Business").Range("B1").Value
 
'This updates and refreshes the PIVOT table
With pt
Field.ClearAllFilters


Field.CurrentPage = NewCat
pt.RefreshTable
End With


'Here you amend to suit your data for second pivot table
Set pt = Worksheets("New Business").PivotTables("PivotTable1")
Set Field = pt.PivotFields("Job No.")
NewCat = Worksheets("New Business").Range("B1").Value
 
'This updates and refreshes the PIVOT table
With pt
Field.ClearAllFilters


Field.CurrentPage = NewCat
pt.RefreshTable
End With
 
End Sub