Your question should have been phrased like this: Is there an English common saying WHICH is identical TO the Chinese proverb --皇帝不急太监急?Or "Does English have a saying which would be identical to the Chinese proverb...?"
The answer would be: "The Onlooker is more anxious than the Player." The Chinese sentence refers to the Emperor and Eunuchs whereas the English sentence uses a sports-related comparison. This is suitable as sports are a high visibility industry in the West, to which English-speakers can easily relate.