אני גר בעיר גדולה.

Yes. גר is the masculine singular form, so it usually means the speaker is male.

• אני גר בעיר גדולה. = said by a male
• אני גרה בעיר גדולה. = said by a female

Hebrew often marks gender in the present tense, unlike English.

Because עיר is a feminine noun in Hebrew. Adjectives usually have to agree with the noun they describe in gender and number.

So:

• עיר גדולה = a big city
• בית גדול = a big house

Here:

• עיר = feminine singular
• גדולה = feminine singular adjective

That is why you do not say עיר גדול.

In Hebrew, adjectives normally come after the noun.

So Hebrew says:

• עיר גדולה literally city big

This is the normal word order for noun + adjective in Hebrew.

Because Hebrew prepositions are often written as prefixes attached to the following word.

Here:

• ב = in
• עיר = city
• בעיר = in a city / in the city, depending on context and vowels

In your sentence, בעיר גדולה means in a big city.

In unpointed Hebrew, the spelling can look very similar, but the meaning depends on whether the noun is indefinite or definite.

• בעיר גדולה = in a big city
• בעיר הגדולה = in the big city

The adjective helps you see the difference:

• גדולה = big
• הגדולה = the big

So in your sentence, because there is no ה on גדולה, the phrase is indefinite: in a big city.

Hebrew has no indefinite article. English uses a/an, but Hebrew usually just uses the noun by itself.

So:

• עיר can mean city or a city
• עיר גדולה = a big city

If Hebrew wants to say the city, it adds ה־:

• העיר = the city
• העיר הגדולה = the big city

Because Hebrew does not use a present-tense form of to be in ordinary sentences like this.

English says:

• I am living
• I am in a big city

Hebrew usually just says:

• אני גר = I live / I am living

So nothing is missing. The sentence is complete without a separate word for am.

It is usually pronounced approximately eer, often transliterated ir or 'ir.

The full sentence can be pronounced roughly like:

ani gar be-ir gdolah

A few pronunciation notes:

• אני = ah-NEE
• גר = gar
• בעיר = beh-EER or be-EER
• גדולה = gdo-LAH

Learners often find עיר tricky because the spelling looks less straightforward than the pronunciation.

Sometimes, but usually אני is helpful.

In the present tense, forms like גר / גרה / גרים / גרות show gender and number, but not always the exact person as clearly as English verb endings do. Because of that, Hebrew often keeps the pronoun when needed for clarity.

So:

• אני גר בעיר גדולה = clear and natural
• גר בעיר גדולה = possible in the right context, but sounds more dependent on context

For a learner, it is safest to include אני.

The verb would change to agree with the subject.

Examples:

• אני גר בעיר גדולה. = I live in a big city.
  said by a male

• אני גרה בעיר גדולה. = I live in a big city.
  said by a female

• אנחנו גרים בעיר גדולה. = We live in a big city.
  mixed group or all males

• אנחנו גרות בעיר גדולה. = We live in a big city.
  all females

Notice that גדולה stays the same here because it agrees with עיר, not with the speaker.