L’elettricista arriva alle nove per controllare il contatore della cucina.

Because elettricista begins with a vowel. In Italian, the singular definite article before a vowel is usually shortened:

• il
  • vowel-starting masculine noun → l’
• la
  • vowel-starting feminine noun → l’

So il elettricista is not correct; it becomes l’elettricista.

The apostrophe shows that the vowel of the article has been dropped.

Elettricista can refer to either a male or a female electrician. It is one of those Italian profession nouns ending in -ista, which can be masculine or feminine depending on the person.

For example:

• l’elettricista è arrivato = the electrician arrived, and the person is male
• l’elettricista è arrivata = the electrician arrived, and the person is female

In your sentence alone, l’elettricista does not by itself clearly show gender.

Because arriva is the conjugated form of the verb, while arrivare is the infinitive.

• arrivare = to arrive
• arriva = he arrives / she arrives / it arrives

Since the subject is l’elettricista, Italian needs the third person singular form:

• L’elettricista arriva = the electrician arrives

Italian usually does not use subject pronouns unless they are needed for emphasis or clarity.

So instead of saying:

• Lui arriva alle nove

Italian normally just says:

• Arriva alle nove

or, as here:

• L’elettricista arriva alle nove

The verb ending often gives enough information, and the subject noun is already stated.

To talk about clock time in Italian, you normally use a + definite article.

So:

• a + le = alle
• alle nove = at nine

Other examples:

• all’una = at one
• alle due = at two
• alle otto = at eight

That is why it is alle nove, not just a nove.

In this context, alle nove means at nine o’clock. Italian often does not need to add the equivalent of o’clock.

So:

• arriva alle nove = arrives at nine / arrives at nine o’clock

Both are natural translations in English.

Per + infinitive often expresses purpose in Italian. It means to, in order to, or for the purpose of doing something.

So:

• per controllare = to check / in order to check

In the sentence:

• L’elettricista arriva alle nove per controllare il contatore della cucina.

the idea is:

• The electrician is arriving in order to check the kitchen meter.

Because after per to express purpose, Italian normally uses the infinitive.

Examples:

• Vengo per aiutare = I’m coming to help
• Esce per comprare il pane = He/she goes out to buy bread
• Arriva per controllare il contatore = He/she arrives to check the meter

So per controllare is the normal structure.

Contatore usually means meter in this kind of sentence, especially a utility meter such as:

• electricity meter
• gas meter
• water meter

Since the sentence is about an electrician, il contatore is most naturally understood as some kind of electrical meter.

It does not mean counter in the sense of a kitchen counter.

Because Italian often uses di + article where English might simply say of the or use a noun more directly.

Here:

• di + la = della
• della cucina = of the kitchen

So il contatore della cucina means the kitchen’s meter or the meter of the kitchen.

Using the article is very common in Italian in these relationships between nouns.

Della is a contraction of:

• di + la = della

This kind of contraction is very common in Italian:

• di + il = del
• di + lo = dello
• di + l’ = dell’
• di + la = della
• di + i = dei
• di + gli = degli
• di + le = delle

So della cucina literally means of the kitchen.

Yes. In Italian, the present tense is often used for a planned or expected future event, especially when there is a time expression.

So:

• L’elettricista arriva alle nove

can mean:

• The electrician arrives at nine
• The electrician is arriving at nine
• The electrician will arrive at nine

The exact English translation depends on context, but the Italian present tense is perfectly normal here.

The sentence breaks down like this:

• L’elettricista = the electrician
• arriva = arrives
• alle nove = at nine
• per controllare = to check
• il contatore della cucina = the kitchen meter / the meter of the kitchen

So the structure is basically:

Subject + verb + time + purpose + object

That makes it a very typical and useful Italian sentence pattern.