尝试：

df1['MATCH'] = df1.apply(lambda x: [i for i, l in zip(df2.ID, df2.LIST_2) if all(v in x['LIST_1'] for v in l)] , axis=1)

print(df1)

图纸：

NAME                      LIST_1       MATCH
0  BILL  [ZF1, ZF2, ZF3, ZF9, ZF11]       [ZB1]
1  PAUL   [ZF1, ZF4, ZF5, ZF2, ZF3]  [ZB1, ZB2]
2  JOHN        [ZF1, ZF2, ZF5, ZF6]       [ZB3]

• 可选 *：如果LIST_1/LIST_2列中的值是字符串，则将它们转换为列表：

from ast import literal_eval

df1.LIST_1 = df1.LIST_1.apply(literal_eval)
df2.LIST_2 = df2.LIST_2.apply(literal_eval)

在pandas中处理Series列表总是很棘手。
最合理的方法可能是使用集合运算：

lst = list(zip(df2['LIST_2'].apply(frozenset), df2['ID']))

df1['MATCH'] = [[ID for s, ID in lst if s.issubset(l)]
                for l in df1['LIST_1']]

输出：

NAME                      LIST_1       MATCH
0  BILL  [ZF1, ZF2, ZF3, ZF9, ZF11]       [ZB1]
1  PAUL   [ZF1, ZF4, ZF5, ZF2, ZF3]  [ZB1, ZB2]
2  JOHN        [ZF1, ZF2, ZF5, ZF6]       [ZB3]