您可以用途：

# reorganize your mapping dictionary
# to have the key: value in correct order
mapper = {k1: {k: v for v, k in d.items()}
          for k1, d in ID_classification.items()}

# map all desired columns
df['id'] = df[list(mapper)].apply(lambda s: s.map(mapper[s.name])).agg('-'.join, axis=1)

# add unique id
df['id'] += '-' + df.groupby('id').cumcount().add(1).astype(str)

输出：

client           type  country potential       id
0  Client 1        Private      USA       low  A-1-1-1
1  Client 2        Private  Ireland      high  A-3-3-1
2  Client 3  Institutional       GB       mid  B-2-2-1
3  Client 4  Institutional       GB       mid  B-2-2-2
4  Client 5  Institutional       GB       mid  B-2-2-3

用途：

#swap key value in inner dictionaries
d = {k:{v1:k1 for k1, v1 in v.items()} for k, v in ID_classification.items()}

#map columns by d with join together by -
s = pd.DataFrame([df[k].map(v) for k, v in d.items()]).agg('-'.join)

#added counter column by Series s
df['id'] = s + '-' + df.groupby(s).cumcount().add(1).astype(str)
print (df)
     client           type  country potential       id
0  Client 1        Private      USA       low  A-1-1-1
1  Client 2        Private  Ireland      high  A-3-3-1
2  Client 3  Institutional       GB       mid  B-2-2-1
3  Client 4  Institutional       GB       mid  B-2-2-2
4  Client 5  Institutional       GB       mid  B-2-2-3