Have a try with some changes. 
Option Explicit
Sub submit2()
    Dim newTab   As String                          '<= added
    If Application.CountBlank(Range("B3:K3")) = 0 Then
        With Rows(3)
            .Copy
            newTab = Range("L3")                    '<= added
            Workbooks.Open Filename:="N:\REPORTING\Liam\MTA Log.xlsm"
            Workbooks("MTA Log.xlsm").Sheets(newTab).Rows(3).Insert '<= changed
            ActiveWorkbook.Close True
            Application.CutCopyMode = False
            .ClearContents
        End With
        Range("C3").Select
        ActiveCell.FormulaR1C1 = "=TEXT(RC[-1],""ddd"")"
        Range("B3").Select
    Else
        MsgBox "Information missing, please make sure all cells are filled before submitting - if no premium enter £0."
    End If
End Sub