您可以将groupby.apply与isin和numpy.where一起使用：

df['Primary Company'] = np.where(
 df.groupby('ID', group_keys=False)
   .apply(lambda g: g['Company'].isin(g.loc[g['Contract Number'].eq(1), 'Company'])
         ),
 'Yes', 'No'
)

输出：

ID  Contract Number Company Primary Company
0  10000                1     Abc             Yes
1  10000                2     Zxc              No
2  10000                3     Abc             Yes
3  10001                1     Zxc             Yes
4  10002                2     Abc              No
5  10002                1     Cde             Yes
6  10002                3     Zxc              No

如果您可以使用布尔值（True/False）代替'Yes'/'No'：

df['Primary Company'] = (
 df.groupby('ID', group_keys=False)
   .apply(lambda g: g['Company'].isin(g.loc[g['Contract Number'].eq(1), 'Company']))
)

筛选Contract Number为1的行，在DataFrame.merge中使用左连接，并比较indicator=True参数生成的_merge列：

mask = (df.merge(df[df['Contract Number'].eq(1)],
                how='left', on=['ID','Company'], indicator=True)['_merge'].eq('both'))
df['Primary Company'] = np.where(mask, 'Yes','No')
print (df)
      ID  Contract Number Company Primary Company
0  10000                1     Abc             Yes
1  10000                2     Zxc              No
2  10000                3     Abc             Yes
3  10001                1     Zxc             Yes
4  10002                2     Abc              No
5  10002                1     Cde             Yes
6  10002                3     Zxc              No

另一个想法是将MultiIndex与Index.isin进行比较：

idx = df[df['Contract Number'].eq(1)].set_index(['ID','Company']).index
df['Primary Company'] = np.where(df.set_index(['ID','Company']).index.isin(idx),
                                 'Yes','No')
print (df)
      ID  Contract Number Company Primary Company
0  10000                1     Abc             Yes
1  10000                2     Zxc              No
2  10000                3     Abc             Yes
3  10001                1     Zxc             Yes
4  10002                2     Abc              No
5  10002                1     Cde             Yes
6  10002                3     Zxc              No