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You can just have a variable that remembers whether the alarm is supposed to be on or off. Let's call it alarm_on. Then:

bool alarm_on;
static void start_alarm() { alarm_on = true; }
static void  stop_alarm() { noTone(); alarm_on = false; }

void loop()
{
    if (alarm_on) alarm();
    if (some_condition()) start_alarm();
    if (some_other_condition()) stop_alarm();
}

For a better approach that allows you to sound the alarm without blocking the whole program, see the Blink Without Delay Arduino tutorial.