One of the play's first stage directions is "The English clock strikes 17 English strokes" (1). This whole "17 strokes" thing already clues us in that there's something fishy going on. So, is it supposed to be 17 o'clock? Over course of the play, the clock goes totally crazy, sometimes striking whenever it pleases, sometimes striking according to the emotions of the characters.
In many ways, the clock becomes just as much of a character as any of the human beings prancing around onstage. All this wacky behavior from the clock seems to symbolize the wackiness of time itself in the play. At many points, it seems as if time doesn't even exist. And, if it does, it's all kinds of messed up.
Shmoop, sobre o simbolismo do relógio em A Cantora Careca, de Eugène Ionesco