How to interpret a sentence with two clauses but no conjunction?
But the sentence above doesn't use a conjunction. In this case, is the sentence valid in grammar?


Conjunctions are often omitted in Chinese and English. The example sentence is valid.


不得到领导的允许，你不能走。
(如果)不得到领导的允许，你(就)不能走。


These two sentences express the same thing. Just the first one omitted 如果 and 就.

You can also omit only 就 and write "如果不得到领导的允许，你不能走。" ; or you can omit only 如果 and write "不得到领导的允许，你就不能走。" . Both sentences are valid.

If you want to express "You couldn't get the permission of the leaders, so you cannot go." the conjunctions would be different- (因為) 你得不到领导的允许，(所以) 你不能走

You can omit 因為 and write "得不到领导的允许，所以你不能走" ; or you can omit 所以 and write "因為得不到领导的允许，你不能走"

but you cannot omit both and not affect the sentence's meaning.

The point is: 


You can omit conjunctions if it doesn't affect the sentence's meaning. 
When a conjunction is needed to clarify the sentence, leave it un-omitted.


Side note:

Beside conjunctions, you can also omit subjects and objects. As long as it doesn't affect the meaning of the sentence. For example: The full reply to "你認得我?" should be " 我認得你" since it is a Q and A between two people, the subject and object can be omitted to make it cleaner, just reply: "認得" is enough.