a bite of the cherry意思是“机会”，那another bite at the cherry就很好理解了，意思是指“又一次机会”。

【例句】
There won't be another bite at the cherry if we screw this up—it's our only chance.
如果我们搞砸了，就不会再有第二次机会了，这是我们唯一的机会。

Jim failed at his first try, but he was lucky enough to have another bite at the cherry.
吉姆第一次尝试没有成功，可幸运的是他还有第二次机会。