How can I understand "3 clauses with only 1 conjunction"?
I found a sentence, 3 clauses with only one conjunction, below, which is totally against my knowledge of grammar.

Confusing sentence: "It's been hard work, but now the business is running smoothly you can sit back and enjoy the fruits of your labours."

source: https://dictionary.cambridge.org/dictionary/english/fruit
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in my opinion:
3 clauses:
clause 1. It's been hard work
clause 2. but now the business is running smoothly
clause 3. you can sit back and enjoy the fruits of your labours.
one conjunction: but

3 clauses should be with "two" conjunction. It will be like --- "It's been hard work, but now the business is running smoothly "SO/AND" you can sit back and enjoy the fruits of your labours."

Since the suspicious sentence is from a dictionary, It should be a perfect sentence. So what is the part I missed? Any keywords or suggestions are all welcomed.
If there is anything wrong in my opinion, please help to correct it. Thank you for your attention.

Question

How can I understand "3 clauses with only 1 conjunction"?
I found a sentence, 3 clauses with only one conjunction, below, which is totally against my knowledge of grammar.

Confusing sentence: "It's been hard work, but now the business is running smoothly you can sit back and enjoy the fruits of your labours."

source: https://dictionary.cambridge.org/dictionary/english/fruit
----
in my opinion:
3 clauses: 
clause 1. It's been hard work
clause 2. but now the business is running smoothly
clause 3. you can sit back and enjoy the fruits of your labours.
one conjunction: but

3 clauses should be with "two" conjunction. It will be like --- "It's been hard work, but now the business is running smoothly "SO/AND" you can sit back and enjoy the fruits of your labours."

Since the suspicious sentence is from a dictionary, It should be a perfect sentence. So what is the part I missed? Any keywords or suggestions are all welcomed.
 If there is anything wrong in my opinion, please help to correct it. Thank you for your attention.

Answer

I’m not as knowledgeable about technical grammar as some of the persons who comment on Italki, but I think the source of the confusion may be this: the sentence has only two independent clauses, and the third clause is a relative clause that really functions as an adjective.  A relative clause is usually introduced by the word “that,” but here the “that” is omitted (see Chris’s comment below, inserting the missing “that”).  One way to understand the sentence is:  “It’s been hard work, but now (that the business is running smoothly) you can sit back and enjoy the fruits of your labors.”   The relative clause that I have put in parentheses can be left out and the sentence is just two clauses joined with a “but” conjunction.  Or, you can include the relative clause to provide, adjectivally, more information about what you mean by “now.”

Answer

There is a comma missing but the sentence is fine.

It's been hard work, but now [that] the business is running smoothly [comma] you can sit back and enjoy the fruits of your labours."

This is equivalent to the following.

It's been hard work.
The business is running smoothly.
You can sit back and enjoy the fruits of your labours.

The word "now" acts as a synonym for "as," "since," or "because."  Without "now," a "so" is needed before the final clause.

It's been hard work, but NOW the business is running smoothly, you can sit back and enjoy the fruits of your labours.

It's been hard work, but the business is running smoothly, SO you can sit back and enjoy the fruits of your labours.