Subtract a year from a datetime column in pandas

Use DateOffset:

df["NEW_DATE"] = df["ACC_DATE"] - pd.offsets.DateOffset(years=1)
print (df)
        ACC_DATE   NEW_DATE
index                      
538   2006-04-07 2005-04-07
550   2006-04-12 2005-04-12

You can use DateOffset to achieve this:

In[88]:
df['NEW_DATE'] = df['ACC_DATE'] - pd.DateOffset(years=1)
df

Out[88]: 
        ACC_DATE   NEW_DATE
index                      
538   2006-04-07 2005-04-07
550   2006-04-12 2005-04-12