If it were not for the departing a/c being on a seperate frequency to the arrival I would suggest that even more timely action could have taken place. The norm is for the departing a/c, after receiving t-off clearance, to monitor TWR until airborne and then switch immediately to the Departure frequency. Because of this procedure the TWR lady had to contact her Departure colleague, explain what was going on and instruct him to turn his outbound traffic. Those extra seconds eats into the seperation.