If the batting team continues to pile on the runs, a second new ball will become available after another 80 overs, so 160 overs in the innings.
In a test match, each innings begins with a new ball and after 80 overs have been bowled, the captain may take a new ball.
Depending on conditions, the captain may delay the new ball. If conditions favor a fast bowler, the new ball will be taken. Spin bowlers usually operate better with a more battered ball.
The batsmen would be informed and the umpire would indicate the new ball to the scorers by raising it for them to see.