It's simple; you can either replace or save a game after editing the Game details. Do so by selecting Save Game... from the Files menu. Replacement requires that the game have been recalled from the database previously. Save Game As... adds the game to the database. Whenever you choose New game the replacement function will be disabled to prevent you from overwriting an existing game with a game that has no moves played yet!
Use Save Game as ... to add the game in a new record to the database. Using this function repeatedly for the same game wastes disk space since you create multiple copies of the same game. The ChessPartner database does not provide for unique game-records.
The save functions allow you to use a compressed format, consuming as little disk space as possible. The time used each move is then not saved in the database, this is only kept using the normal format which also uses a larger format to store the move list.