Have a following DataFrame:

df = pd.DataFrame({"booking": ['A', 'B', 'C'],
                   "route": [['1','2','3'],['5','4','1'],['3','6','8']]})

1. need to insert into each "route" cell the ‘0’ at the beginning of list to get this:

df1 = pd.DataFrame({"booking": ['A', 'B', 'C'],
                    "route": [['0','1','2','3'],['0','5','4','1'],['0','3','6','8']]})

2. and next step is to split route by legs, to get this:

df1 = pd.DataFrame({"booking": ['A', 'B', 'C'],
                    "legs": [['0>1','1>2','2>3'],['0>5', '5>4','4>1'],['0>3','3>6','6>8']]})

>Solution :

You can use list comprehensions:

df1 = df.assign(route=[[0]+l for l in df['route']])

Output:

  booking         route
0       A  [0, 1, 2, 3]
1       B  [0, 5, 4, 1]
2       C  [0, 3, 6, 8]

Then:

df1 = df.assign(route=[[f'{a}>{b}' for a,b in zip(l, l[1:])]
                       for l in df1['route']])

Output:

  booking            route
0       A  [0>1, 1>2, 2>3]
1       B  [0>5, 5>4, 4>1]
2       C  [0>3, 3>6, 6>8]

Of course, as commented by @Nick, you can use a single step if the intermediate is not needed:

df1 = df.assign(route=[[f'{a}>{b}' for a,b in zip([0] + l, l)]
                       for l in df['route']])

Output:

  booking            route
0       A  [0>1, 1>2, 2>3]
1       B  [0>5, 5>4, 4>1]
2       C  [0>3, 3>6, 6>8]