Some problems with your function:
- A formula returns a value. It is not used to alter other properties/cells of a worksheet.
- Hence you should set your results to the function; not try to write to a range
 
- Dim k, l, m  As Integeronly declares- mas- Integer,- kand- lare unspecified so they will be declared as a variant.
- The constructed array will be horizontal. If you want the results vertical, you need to Transposeit, or create a 2D array initially.
- Option Base 1 is unnecessary since you explicitly declare the lower bound
Assuming you want to use this function on a worksheet, TestIt sets things up.
Note2: The formula on the worksheet assumes you have Excel with dynamic arrays. If you have an earlier version of Excel, you will need to have a different worksheet formula
See your modifed function and TestIt:
Modified with Transpose added to worksheet formula
Option Explicit
Function Takseer(Rg As Variant)
    Dim NewArray() As Variant
    Dim StrEx As String
    Dim k As Long, l As Long, m  As Long
    StrEx = Rg
    StrEx = WorksheetFunction.Substitute(StrEx, " ", "")
    m = Len(StrEx)
    For k = 1 To m
        ReDim Preserve NewArray(1 To m)
            NewArray(k) = Mid(StrEx, k, 1)
    Next k
    Takseer = NewArray
End Function
Sub TestIt()
    [a1] = "abcdefg"
    [c1].EntireColumn.Clear
    [c1].Formula2 = "=Transpose(Takseer(A1))"
End Sub
Modified to create 2d vertical array
can't really use redim preserve on this array.  And I prefer to avoid it anyway because of the overhead
Option Explicit
Function Takseer(Rg As Variant)
    Dim NewArray() As Variant, col As Collection
    Dim StrEx As String
    Dim k As Long, l As Long, m  As Long
    StrEx = Rg
    StrEx = WorksheetFunction.Substitute(StrEx, " ", "")
    m = Len(StrEx)
    
    Set col = New Collection
    For k = 1 To m
        col.Add Mid(StrEx, k, 1)
    Next k
    
    ReDim NewArray(1 To col.Count, 1 To 1)
    For k = 1 To col.Count
        NewArray(k, 1) = col(k)
    Next k
    
    Takseer = NewArray
End Function
Sub TestIt()
    [a1] = "abcdefg"
    [c1].EntireColumn.Clear
    [c1].Formula2 = "=Takseer(A1)"
End Sub

Note:
- TestItis merely to test the function. You should enter the appropriate formula yourself, either manually or programmatically, into the destination range.
- If you do not have dynamic arrays, then you would need to enter an array formula into the destination range; or a formula using the INDEXfunction to return each element of the array.
- In TestIt, you might change the line that puts the formula onto the worksheet toRange(Cells(1, 3), Cells(Len([a1]), 3)).FormulaArray = "=Takseer(a1)", but, again, it is anticipated that you would be entering the correct formula onto your worksheet manually or programmatically anyway.