Please ignore my comment, as I just realize that it will be a different result if in column A there is a cell with the same value.
Example Data :

Expected result after running the sub :

Sub test()
Dim rgHdr As Range: Dim rgData As Range: Dim cell As Range
Dim i As Integer: Dim arr: Dim ins As Integer:dim sh as worksheet
Set sh = Sheets("Sheet1") 'change if needed
ins = 3 'change if needed
With sh
.Range("A1").EntireRow.Resize(ins).Insert Shift:=xlDown
Set rgHdr = .Range("A1").EntireRow.Resize(1 + ins)
Set rgData = .Range("K" & 2 + ins, .Range("K" & Rows.Count).End(xlUp))
End With
Set arr = CreateObject("scripting.dictionary")
For Each cell In rgData: arr.Item(cell.Value) = 1: Next
For i = 1 To arr.Count - 1
rgHdr.Copy
sh.Cells(rgData.Find(arr.Keys()(i), _
after:=rgData.End(xlDown)).Row, 1).Insert Shift:=xlDown
Next
sh.Range("A1").EntireRow.Resize(ins).Delete
End Sub
sh = the sheets where the data is.
ins = skip how many blank rows.
The code use "insert copied cells" method, so it make three blank rows (the value of ins) before the header, then set the first three rows as rgHdr, set the rgData from K2 down to the last row with value.
arr = unique value in column K.
then it loop to each element in arr, get the first row occurence of the found cell which value is the looped element in arr, insert the copied rgHdr to that row.
Then finally it delete those three (ins value is 3) additional blank rows.