השותף הקודם שלי עבר לעיר אחרת, ועכשיו אני צריכה לחלוק את שכר הדירה עם שותפה חדשה.

In isolation, שותף can mean partner, associate, or roommate/flatmate. In this sentence, because of שכר הדירה (the rent), it clearly means roommate.

• שותף = male roommate / male partner
• שותפה = female roommate / female partner

So here:

• השותף הקודם שלי = my previous male roommate
• שותפה חדשה = a new female roommate

Because of צריכה.

In the present tense, Hebrew words like צריך / צריכה agree with the speaker’s gender:

• אני צריך = I need (male speaker)
• אני צריכה = I need (female speaker)

So ועכשיו אני צריכה... tells you the speaker is female.

Because they refer to two different people, and Hebrew marks gender on nouns.

• השותף הקודם שלי = my previous male roommate
• שותפה חדשה = a new female roommate

So the old roommate is male, and the new roommate is female.

This is about definiteness.

• השותף הקודם שלי = my previous roommate → definite
• שותפה חדשה = a new roommate → indefinite

In Hebrew, if a noun is definite, its adjective is also definite:

• השותף הקודם = the previous roommate
• השותפה החדשה = the new female roommate

But here the second phrase is not the new roommate; it is a new roommate, so there is no ה-:

• שותפה חדשה = a new female roommate

That is the normal Hebrew pattern.

Hebrew usually says:

• השותף שלי = my roommate
• הדירה שלי = my apartment
• הספר שלי = my book

So instead of putting my before the noun, Hebrew usually uses של + pronoun after the noun.

Yes, the phrase is definite in meaning, but Hebrew commonly still uses ה- with nouns followed by שלי / שלך / שלו etc.

So Hebrew normally says:

• השותף שלי
• הבית שלי
• החברה שלי

and not usually:

• שותף שלי
• בית שלי

So השותף הקודם שלי is the normal way to say my previous roommate.

It often does mean passed or crossed, but in context it can also mean moved.

Here:

• עבר לעיר אחרת = moved to another city

So the idea is that the old roommate relocated.

Grammatically, עבר is past tense, masculine singular, matching השותף.
If the subject were feminine, it would be עברה.

There are two things happening here:

1. ל- means to

   • לעיר = to a city / to the city

2. עיר is a feminine noun, so אחר becomes אחרת

   • עיר אחרת = another city

So:

• עבר לעיר אחרת = moved to another city

שכר הדירה is a fixed Hebrew expression meaning the rent.

Literally, it is something like:

• שכר = payment / fee / rent
• הדירה = the apartment

Together, שכר הדירה means the apartment rent, which in natural English is just the rent.

This is a kind of Hebrew noun connection called a construct phrase.

Because שכר הדירה is a definite direct object.

Hebrew uses את before a direct object when it is definite:

• אני רואה את הבית = I see the house
• אני קוראת את הספר = I am reading the book
• אני צריכה לחלוק את שכר הדירה = I need to share the rent

את does not really translate into English; it is just a grammar marker.

Because in Hebrew construct phrases, definiteness is usually shown on the second noun, and it makes the whole phrase definite.

So:

• שכר דירה = rent / apartment rent
• שכר הדירה = the rent

The ה- appears on דירה, but the whole phrase becomes definite.

Yes, Hebrew can sometimes leave it out, but אני is very natural here.

In the present tense, forms like צריך / צריכה show gender and number, but not as clearly as past or future forms show person. Because of that, Hebrew often includes the pronoun:

• ועכשיו אני צריכה... = and now I need...
• ועכשיו צריכה... would usually sound incomplete unless the context is very clear

So including אני is normal and helpful.

Yes. Here לחלוק means to share or to split.

In this sentence:

• לחלוק את שכר הדירה עם שותפה חדשה = to share / split the rent with a new roommate

So it does not mean sharing in a vague emotional sense; it means dividing the rent between the two roommates.

Only the part that agrees with the speaker would need to change:

• ועכשיו אני צריך לחלוק את שכר הדירה עם שותפה חדשה.

So:

• אני צריכה = I need (female speaker)
• אני צריך = I need (male speaker)

Everything else could stay the same if the old roommate is male and the new roommate is female.