1### first get max row number ###
2max_row = df.shape[0]
3### the append to (max_row + 1) without header ###
4df.to_excel("file.xlsx",sheet_name="sheetname",startrow=max_row+1,header=False,index=False)
5### if you have index column in your excel file ###
6 ### then you can just set index=True ###