I have a sample from my dataframe:
Created Insert Time MatchKey In Previous New Type 18593 2016-08-12 2018-02-19 LXGS0903
You can use pd.Series.mask for exactly this purpose:
df['New Type'].mask(df['In Previous']=='Yes', 'In Previous', inplace=True)
Somewhat confusingly, you have to remember that pd.Series.mask updates a value when a condition is met, while pd.Series.where updates a value when a condition is not met.
pd.Series.mask
pd.Series.where