Below I've provided a fully reproducible example of how you can go about modifying an existing .xlsx workbook using pandas and the openpyxl module (link to Openpyxl Docs).

First, for demonstration purposes, I create a workbook called test.xlsx:

from openpyxl import load_workbook
import pandas as pd
writer = pd.ExcelWriter('test.xlsx', engine='openpyxl') 
wb  = writer.book
df = pd.DataFrame({'Col_A': [1,2,3,4],
                  'Col_B': [5,6,7,8],
                  'Col_C': [0,0,0,0],
                  'Col_D': [13,14,15,16]})

df.to_excel(writer, index=False)
wb.save('test.xlsx')

This is the Expected output at this point:

In this second part, we load the existing workbook ('test.xlsx') and modify the third column with different data.

from openpyxl import load_workbook
import pandas as pd
df_new = pd.DataFrame({'Col_C': [9, 10, 11, 12]})
wb = load_workbook('test.xlsx')

ws = wb['Sheet1']

for index, row in df_new.iterrows():
    cell = 'C%d'  % (index + 2)
    ws[cell] = row[0]

wb.save('test.xlsx')

This is the Expected output at the end:

Ok, startcol was the answer!

pd_array.to_excel(r'C:\Users\my_dir\SandBox.xlsx', sheet_name='Sheet2', startcol= 8)

UPDATE2: appending data to existing Excel sheet, preserving other (old) sheets:

import pandas as pd
from openpyxl import load_workbook

fn = r'C:\Temp\.data\doc.xlsx'

df = pd.read_excel(fn, header=None)
df2 = pd.DataFrame({'Data': [13, 24, 35, 46]})

writer = pd.ExcelWriter(fn, engine='openpyxl')
book = load_workbook(fn)
writer.book = book
writer.sheets = dict((ws.title, ws) for ws in book.worksheets)

df.to_excel(writer, sheet_name='Sheet1', header=None, index=False)
df2.to_excel(writer, sheet_name='Sheet1', header=None, index=False,
             startcol=7,startrow=6)

writer.save()

UPDATE: your Excel file doesn't have a header, so you should process it accordingly:

In [57]: df = pd.read_excel(fn, header=None)

In [58]: df
Out[58]:
     0    1
0  abc  def
1  ghi  lmn

In [59]: df2
Out[59]:
   Data
0    13
1    24
2    35
3    46

In [60]: writer = pd.ExcelWriter(fn)

In [61]: df.to_excel(writer, header=None, index=False)

In [62]: df2.to_excel(writer, startcol=7,startrow=6, header=None, index=False)

In [63]: writer.save()

OLD answer:

You can use the following trick:

first read the existing contents of the excel file into a new DF:

In [17]: fn = r'C:\Temp\b.xlsx'

In [18]: df = pd.read_excel(fn)

In [19]: df
Out[19]:
       A      B     C      D
0   val1    NaN  val3   val4
1  val11  val22   NaN  val33

now we can write it back and append a new DF2:

In [20]: writer = pd.ExcelWriter(fn)

In [21]: df.to_excel(writer, index=False)

In [22]: df2.to_excel(writer, startcol=7,startrow=6, header=None)

In [23]: writer.save()

Say for example, you have dataframe with 3 columns whose column names are "animals","column_1", "column_2". If you need only column_1 and column_2 to be exported as xlsx file, you can do as shown below,

df = pd.DataFrame(data=[['dog','a','b'],['cat','b','c'],['dog','c','a']],columns=(['animal','column1','column2']))
df[['column1','column2']].to_excel('"output.xlsx"')

I pulled this from my script and edited in your keywords. This works for me. I use openpyxl.

from openpyxl import load_workbook

wb = load_workbook("P:\TestResultSheet.xlsx")
ws = wb["TestResult"]
ws.write('C2', result_df.query("Jira_Num == 'XXXX-01' ")["TestQuery"])
workbook.close()

using df.to_excel should be much easier

df.to_excel('c:\users\3619678\desktop\example_file.xls', sheet_name='sheet1', float_format = "%.2f")

https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.to_excel.html

[Edit] It looks like this may not be good enough. based on the xlwt documentation, there may not be a tool out there that you want to use. As such, I've added headers and an easy way for you to format by column

import pandas as pd

# Example Dataframe
df = pd.DataFrame({'Numbers': [1000, 2000, 3000, 4000, 5000],
                   'Names': ['Adam','Blake','Chad','Drake','Erak'],
                   'Weights': [1.05, 2.10, 3.15, 4.20, 5.25],
})

import xlwt

# Create a workbook and add a worksheet
workbook = xlwt.Workbook('example_file.xls')
worksheet = workbook.add_sheet('sheet1',cell_overwrite_ok=True)

# Create dictionary of formats for each column
number_format = xlwt.easyxf(num_format_str='0.00')
cols_to_format = {0:number_format}

for z, value in enumerate(df.columns):
    worksheet.write(0, z, value)

# Iterate over the data and write it out row by row
for x, y in df.iterrows():
    for z, value in enumerate(y):
        if z in cols_to_format.keys():
            worksheet.write(x + 1, z, value, cols_to_format[z])
        else: ## Save with no format
             worksheet.write(x + 1, z, value)

# Save/output the workbook
workbook.save('example_file.xls')