Combining continuous dates from two columns in pandas data frame

You could also try with for-loops and df.loc[]

for start in df.statr_date:
    for end in df.end_date:
        if start==end:
            df.loc[df[df.end_date.eq(end)].index, 'end_date'] = df.loc[df[df.statr_date.eq(start)].index, 'end_date']
            df = df.drop(df[df.statr_date.eq(start)].index)


Output:
    ID  Order_ID           statr_date             end_date Product Sub_Product
0  746         1  08-Oct-2019 0:00:00  17-Dec-2019 0:00:00     LPP         Abc
1  746         2  10-Oct-2019 0:00:00  02-Sep-2020 0:00:00     LPP         Abc
2  746         3  10-Oct-2019 0:00:00  11-Sep-2020 0:00:00     LPP         Abc
3  746         4  10-Oct-2019 0:00:00  08-Jan-2021 0:00:00     LPP         Abc

Edit: This solution with multiple for-loops won't be very performance-friendly for large data

# Input Data
   ID  Order_ID           statr_date             end_date Product Sub_Product
0  746         1  08-Oct-2019 0:00:00  16-Nov-2019 0:00:00     LPP         Abc
1  746         2  10-Oct-2019 0:00:00  02-Sep-2020 0:00:00     LPP         Abc
2  746         3  10-Oct-2019 0:00:00  11-Sep-2020 0:00:00     LPP         Abc
3  746         4  10-Oct-2019 0:00:00  08-Jan-2021 0:00:00     LPP         Abc
4  746         5  16-Nov-2019 0:00:00  17-Dec-2019 0:00:00     LPP         Abc
5  756         6  11-Oct-2019 0:00:00  05-Sep-2020 0:00:00     LBB         Abc
6  756         7  10-Nov-2019 0:00:00  11-Dec-2020 0:00:00     LBB         Abc
7  766         8  22-Oct-2019 0:00:00  19-Nov-2019 0:00:00     LBB         Abc
8  766         9  19-Nov-2019 0:00:00  27-Dec-2019 0:00:00     LBB         Agn


g = df.groupby(['ID','Product', 'Sub_Product'])

dfs = []
for group in g.groups:
    df1 = g.get_group(group)
    for start in df1.statr_date:
        for end in df1.end_date:
            if start==end:
                df1.loc[df1[df1.end_date.eq(end)].index, 'end_date'] = df1.loc[df1[df1.statr_date.eq(start)].index, 'end_date']
                df1 = df1.drop(df1[df1.statr_date.eq(start)].index)
    
    dfs.append(df1)                

out = pd.concat(dfs).reset_index()
out

Output:

   index   ID  Order_ID           statr_date             end_date Product  \
0      0  746         1  08-Oct-2019 0:00:00  17-Dec-2019 0:00:00     LPP   
1      1  746         2  10-Oct-2019 0:00:00  02-Sep-2020 0:00:00     LPP   
2      2  746         3  10-Oct-2019 0:00:00  11-Sep-2020 0:00:00     LPP   
3      3  746         4  10-Oct-2019 0:00:00  08-Jan-2021 0:00:00     LPP   
4      5  756         6  11-Oct-2019 0:00:00  05-Sep-2020 0:00:00     LBB   
5      6  756         7  10-Nov-2019 0:00:00  11-Dec-2020 0:00:00     LBB   
6      7  766         8  22-Oct-2019 0:00:00  19-Nov-2019 0:00:00     LBB   
7      8  766         9  19-Nov-2019 0:00:00  27-Dec-2019 0:00:00     LBB   

You can take a look at each pairwise combination of rows and then compare the start date of one row with the end date of another row to see if they fit the pattern

import numpy as np
from itertools import combinations

start_dates = pd.to_datetime(df['statr_date'])
end_dates = pd.to_datetime(df['end_date'])
order_ids = df['Order_ID']

dates = [(o, s, e) for o, s, e in zip(order_ids, start_dates, end_dates)]
od_map = dict.fromkeys(order_ids, np.nan)

for combo in combinations(dates, 2):
    ((order_first, start_first, end_first), (order_second, start_second, end_second)) = combo
    if end_first == start_second:
        od_map[order_first] = od_map[order_second] = min(order_first, order_second)

df['od_grp'] = df['Order_ID'].map(od_map).fillna(df['Order_ID'])
df_grp = df.groupby('od_grp').agg({'statr_date': 'min', 'end_date': 'max'})
print(df_grp)
#                 statr_date             end_date
#od_grp                                          
#1.0     08-Oct-2019 0:00:00  17-Dec-2019 0:00:00
#2.0     10-Oct-2019 0:00:00  02-Sep-2020 0:00:00
#3.0     10-Oct-2019 0:00:00  11-Sep-2020 0:00:00
#4.0     10-Oct-2019 0:00:00  08-Jan-2021 0:00:00