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Today I read a sentence below:

The employment rate has continued to rise in big cities thanks to the efforts of the local governments to increase it.

Why is there a "to" used before word "increase", it reads hard, does this sentence wrong? Cause there is a "thanks to" in this sentence?

If you want a simple answer, I'm afraid I don't have one for you. In English the infinitive of a verb, words like "to play", "to walk" or "to think" can be used as "to-infinitives" (where the particle 'to' is included), and "bare-infinitives" (without the particle 'to'). The bare-infinitives are the headwords of dictionaries.

When you can use one or the other depends on specific rules, which are outlined in this Wikipedia article, which shows when you can use the to-infinitive or the bare-infinitive bare-infinitives.

Cases where the "bare-infinitive" is allowed is in constructions like:

I can to speak English.

I will to go to bed.

The loud bang made me to jump.

If you follow that article I linked you'll come down to a list of examples where the "to-infinitive" must be used. It shows:

As a modifier of certain nouns and adjectives:

the reason to laugh
the effort to expand
anxious to get a ticket
to-infinitive

In certain cases you can reform the construction by using "of + present participle", such as "I made the effort of trying it."

If you go to this site, which is a grammar checker, and copy and paste the following in:

I made the effort leave my school. I made the effort of leaving my
school. I made the decision stop my habit. I made the decision of
stopping my habit.

You'll see that it highlights "effort leave" and "decision stop", as there needs to be the particle "to" in between the two words.

In your sentence the "thanks to" means the same thing as "due to" or "because of". This part does not have any bearing on whether "to" needs to be included. Think of the following sentences and ask yourself if they are grammatical:

I made the effort clean my room.

He made a strong effort win the competition.

It makes no difference in this case if it's the efforts of the government, an effort or a decision or an attempt is generally "to do" something, ie., a "to-infinitive" verb,

Here are some dictionary entries for the use of "effort".

2.It was an effort to get up.

3.Make an effort to arrive promptly.
American Heritage Dictionary

2.a our effort to save him failed.
Collins English Dictionary

A to is required for the sentence to make grammatical sense regardless of the thanks to.

thanks to the efforts of the local government to increase it

There are three modifiers attached to the noun "efforts": the definite article, a prepositional phrase, and an infinitive phrase.  The entire noun phrase "the efforts of the local government to increase it" is the object of the preposition "to", which attaches this noun phrase to the word "thanks". 

Let's look at what happens without the "to" before "increase":

The efforts of the local government increase it.

This is a complete independent clause.  Without the "to", "increase" works as a finite verb.  It has tense.  It creates a predicate which requires a subject.  This version can stand as a sentence on its own.  It cannot act as the object of "thanks to". 

The infinitive phrase "to increase it" represents the purpose of the efforts.  The predicate "increase it" would represent the action of the efforts. 

Without the "to" before "increase", we're left with a clause that does not attach to the prior clause, leaving the sentence broken.  We're also left with a clause that carries a different meaning than the noun phrase in the original version of the sentence. 

With the "to" before "increase", we're left with a noun phrase that acts as the object of the "to" after "thanks".  The sentence is coherent.  The meaning is clear.