Let's assume you have this data in order to simulate the shape of your DataFrames:
df_one = pd.DataFrame(data=np.linspace(1, 297, 297), columns=["one"])
df_two = pd.DataFrame(data=np.linspace(101, 159, 59), columns=["two"])
You can create an empty DataFrame with a shape of df_one.shape[0] minus df_two.shape[0]:
data_nan = [np.nan for _ in range(df_one.shape[0] - df_two.shape[0])]
df_nan = pd.DataFrame(data=data_nan, columns=["two"])
Then create a temporary Dataframe with pd.concat:
# df_nan in first place so non NaN values will be in the bottom part
# .reset_index(drop=True) to keep indexes consistency
df_tmp = pd.concat([df_nan, df_two]).reset_index(drop=True)
And in the end...
# axis = 1 because you want to "append" a new column, not rows
df = pd.concat([df_one, df_tmp], axis=1).reset_index(drop=True)