אם הקוד לא עובד, תתקשרי למזכירה והיא תשלח קוד חדש.

Because the speaker is talking to one female.

תתקשרי is the 2nd person feminine singular form of להתקשר (to call / to phone).

Related forms:

• תתקשר = to one male
• תתקשרי = to one female
• תתקשרו = to more than one person

So this sentence is specifically addressed to a woman.

Good question. התקשרי is the formal imperative form: Call! said to one woman.

But in modern spoken Hebrew, people very often use the future form instead of the classical imperative:

• תתקשרי = call
• תתקשר = call
• תתקשרו = call

So תתקשרי here is functioning like a command or instruction, even though it is technically a future form.

אם means if.

So:

• אם הקוד לא עובד = if the code doesn’t work

It introduces the condition, just like if in English.

Hebrew often does not need an explicit word for then in this kind of sentence.

So:

• אם הקוד לא עובד, תתקשרי...
  naturally means
• If the code doesn’t work, call...

You can sometimes add אז for then, but it is often omitted because the meaning is already clear.

לא is the normal word for not.

עובד literally means working or works, depending on context. In Hebrew, the present tense often uses a participle-like form, so:

• הקוד עובד = the code works / the code is working
• הקוד לא עובד = the code doesn’t work / the code isn’t working

So Hebrew uses:

• לא + present form

Because קוד is a masculine singular noun.

In Hebrew, the present-tense form agrees with the noun in gender and number:

• הקוד עובד = the code works
• התוכנה עובדת = the software works

So עובד matches קוד because קוד is masculine.

Because ה־ is the Hebrew definite article, meaning the.

• הקוד = the code
• קוד חדש = a new code

So the first code is a specific code already being talked about, while the second one is indefinite: a new code.

If Hebrew wanted to say the new code, it would be:

• הקוד החדש

Notice that the adjective also becomes definite.

Because in Hebrew, adjectives usually come after the noun.

So:

• קוד חדש = new code
• מזכירה טובה = good secretary

This is the normal word order in Hebrew.

Also, the adjective must agree with the noun:

• קוד חדש = masculine singular
• קודים חדשים = masculine plural
• הקוד החדש = definite masculine singular

It is the preposition ל־ attached to מזכירה.

So:

• ל־ = to
• מזכירה = secretary (female)

Together:

• למזכירה = to the secretary or to a secretary, depending on context and pronunciation

In unpointed Hebrew spelling, both can look the same:

• למזכירה can be read as lemazkira = to a secretary
• or lamazkira = to the secretary

Usually the context tells you which one is meant. In this sentence, the meaning is probably to the secretary.

Yes, Hebrew often can drop subject pronouns. But here היא is very natural.

Why include it?

• the subject changes from you in תתקשרי
• to she in היא תשלח

So היא makes the switch clear:

• תתקשרי למזכירה והיא תשלח... = call the secretary and she will send...

Without היא, the sentence could still work in some contexts, but adding it makes the meaning clearer and smoother.

Because in the Hebrew future tense, ת־ is used for several different persons.

For the verb לשלוח (to send):

• אני אשלח = I will send
• אתה תשלח = you (masc. sg.) will send
• את תשלחי = you (fem. sg.) will send
• היא תשלח = she will send
• הוא ישלח = he will send

So תשלח by itself could mean either:

• you will send (masculine singular)
• or she will send

Here, היא makes it clear that it means she will send.

Yes. ו־ means and.

So:

• והיא תשלח קוד חדש = and she will send a new code

In this sentence, it links the next result in the sequence:

• If the code doesn’t work, call the secretary, and she will send a new code.

So it is ordinary and, but in context it also helps move the sentence forward logically.