העובדת במחלקה שלי התפטרה בשבוע שעבר, ולכן מחפשים עכשיו עובדת אחרת.

Here העובדת means the female employee.

That form can also be the feminine singular present form of לעבוד and mean working / works, but in this sentence it is clearly a noun. The structure העובדת במחלקה שלי is a noun phrase, and the actual verb of the clause is התפטרה.

Because the employee being talked about is female. Hebrew marks gender much more often than English does.

You can see feminine singular agreement in several words:

• עובדת = female employee
• התפטרה = she resigned
• עובדת אחרת = another female employee

So the grammar is matching the gender of the person being discussed.

Literally it is:

• ב־ = in
• מחלקה = department
• שלי = my / of mine

So the whole phrase means in my department.

Hebrew often expresses possession as noun + שלי, literally something like department of mine.

That is the normal Hebrew pattern. Hebrew usually says:

• הבית שלי = my house
• המורה שלי = my teacher
• המחלקה שלי = my department

So unlike English, the possessive word usually comes after the noun.

התפטרה means resigned, as in she quit her job.

It is the past-tense, feminine singular form of להתפטר.

This is different from being fired. If the employer fired her, you would say something like:

• פיטרו אותה = they fired her
• היא פוטרה = she was fired

So התפטרה specifically means that she left by her own decision.

בשבוע שעבר means last week.

Breaking it down:

• ב־ = in / during
• שבוע = week
• שעבר = past / that passed

In Hebrew, descriptive words usually come after the noun, so שבוע שעבר is literally week past. That is the normal Hebrew order.

ולכן means and therefore, and so, or simply so.

It is made of:

• ו־ = and
• לכן = therefore

So the sentence is linking the two ideas: the employee resigned, therefore they are now looking for someone else.

Hebrew often uses third-person plural to mean an unspecified they or people.

So מחפשים עכשיו... literally means they are looking now..., but it really means something like:

• they’re looking
• people are looking
• someone is looking
• they are searching

This is a very common Hebrew way to make a general or impersonal statement.

Because מחפשים is not agreeing with עובדת. It is referring to the unnamed people who are doing the searching.

In Hebrew, when that group is unspecified, the masculine plural is usually used as the default form. So מחפשים here means they are looking, not female employees are looking.

Because the Hebrew verb לחפש works differently from English to look for.

In English, you say look for someone.
In Hebrew, לחפש usually takes a direct object without a preposition:

• מחפשים עובדת = they are looking for an employee
• אני מחפש את המפתחות = I am looking for the keys

So Hebrew does not need a separate word equivalent to English for here.

Hebrew usually prefers to repeat the noun when it is important for clarity.

So מחפשים עכשיו עובדת אחרת clearly means they are now looking for another female employee.

If you said only אחרת, it could sound incomplete here. You could say מישהי אחרת in some contexts, but that would mean someone else, which is a little less specific than another employee.

Here אחרת means another or a different one.

It is the feminine singular form of אחר, and it agrees with עובדת:

• עובד אחר = another male employee
• עובדת אחרת = another female employee

So it is not a separate adverb here; it is an adjective describing the noun.

Yes. Hebrew word order is fairly flexible, especially with adverbs like עכשיו.

This sentence says:

• מחפשים עכשיו עובדת אחרת

But these would also be natural in many contexts:

• עכשיו מחפשים עובדת אחרת
• מחפשים עובדת אחרת עכשיו

The version in your sentence sounds very natural and puts now right after the verb.

It would become:

העובד במחלקה שלי התפטר בשבוע שעבר, ולכן מחפשים עכשיו עובד אחר.

Notice the changes:

• העובדת → העובד
• התפטרה → התפטר
• עובדת אחרת → עובד אחר

But מחפשים stays the same, because it still means the unspecified they are looking.