let's start with a function
table1 = pd.DataFrame({'Avg1':[1,2,3,4],'Avg2':[3,5,1,15],'Date':['2021-08-06','2021-08-07','2021-08-08','2021-08-09']})
df2 = pd.DataFrame({'Return Avg':['Avg1','Avg2'],'At Date':['2021-08-08','2021-08-07']})
def get_the_currect_value(date, col_name, ext_table):
return ext_table.loc[ext_table['Date'] == date, col_name].iloc[0]
now after the function, we will use apply to create the new column you want
df2['rv'] = df2.apply(lambda x: get_the_currect_value(x['At Date'],x['Return Avg'], table1),axis=1)
and that it