Náš nový byt je drahý, ale náš starý byt byl levný.

Because the sentence contrasts present and past.

• je = is → present tense of být (to be), 3rd person singular
  
  • Náš nový byt je drahý = Our new flat is expensive (now).
• byl = was → past tense of být, masculine singular
  
  • náš starý byt byl levný = our old flat was cheap (in the past).

So the grammar mirrors the time contrast in English: is vs was → je vs byl.

In Czech, past tense forms of být agree with the gender and number of the subject.

The subject here is byt (flat), which is:

• gender: masculine inanimate
• number: singular

So you must use:

• byl – masculine singular

Other options:

• byla – feminine singular (e.g. žena byla – the woman was)
• bylo – neuter singular (e.g. auto bylo – the car was)
• byli/byly – plurals depending on the gender mix

Because byt is masculine singular, byl is the correct form.

You don’t have to repeat náš. Repetition is possible but not required.

Your sentence is:

• Náš nový byt je drahý, ale náš starý byt byl levný.

More natural and less repetitive versions:

• Náš nový byt je drahý, ale starý byl levný.
• Náš nový byt je drahý, ale ten starý byl levný.
  (ten = that)

You usually:

• Say náš once to establish whose flat it is.
• Then drop it, unless you want extra emphasis (e.g. contrasting our flat with someone else’s flat).

So repeating náš is correct, but not necessary.

You can omit byt in the second part, and native speakers often do:

• Náš nový byt je drahý, ale starý byl levný.

Here, starý (old) and byl (was) clearly refer back to byt from context.

Saying byt twice is:

• Grammatically fine.
• Slightly more formal or heavy.
• Sometimes used for clarity or emphasis.

In everyday speech, omitting the repeated noun is more natural when the meaning is obvious.

Because they are all:

• Adjectives describing byt
• In nominative case
• Masculine singular (matching the gender/number of byt)

Byt = masculine inanimate noun → nominative singular.

So adjectives must agree:

• náš (our) – masculine singular nominative
• nový (new) – masculine singular nominative
• starý (old) – masculine singular nominative
• drahý (expensive) – masculine singular nominative
• levný (cheap) – masculine singular nominative

If the noun were feminine or plural, the endings would change, for example:

• naše nová kuchyně je drahá – our new kitchen is expensive (feminine sg.)
• naše nové byty jsou drahé – our new flats are expensive (plural)

Byt here is:

• Gender: masculine inanimate
• Number: singular
• Case: nominative

Reason:

• It is the subject of both clauses:
  • (Náš nový) byt je drahý
  • (náš starý) byt byl levný

Subjects normally appear in the nominative in Czech, just like in most Indo‑European languages.

They are all forms of “our”, but they change according to gender, number, and case of the noun they modify.

In the basic nominative singular:

• náš – masculine singular (e.g. náš byt – our flat)
• naše – feminine singular or neuter singular (e.g. naše kuchyně – our kitchen, naše auto – our car)
• naši – masculine animate plural (e.g. naši kamarádi – our (male) friends)

In your sentence:

• byt is masculine singular → náš byt is required.

In Czech, you normally put a comma before “ale” when it connects two clauses (two parts that each have their own verb):

• Náš nový byt je drahý,
  ale náš starý byt byl levný.

Each part has its own verb (je, byl), so you join two independent clauses with , ale.

If ale only connected shorter phrases inside one clause, the comma might not be needed, but here it clearly separates two full statements.

Czech word order is more flexible than English, because grammatical roles are shown by endings, not position.

Your original:

• Náš nový byt je drahý, ale náš starý byt byl levný.

You can change the word order for emphasis, for example:

• Náš nový byt je drahý, ale levný byl náš starý byt.
  → Emphasis on levný (cheap).
• Drahý je náš nový byt, ale levný byl ten starý.
  → Very strong contrast of drahý vs levný.

All these are grammatical, but:

• The neutral, most common order is the original one: subject – verb – complement.
• Unusual orders sound more emphatic, contrastive, or stylistic.

In standard Czech, in the third person present tense, you normally keep the verb “to be”:

• Náš nový byt je drahý – correct, natural.
• Náš nový byt drahý – feels incomplete or very stylized, like a note or a headline.

Unlike Russian, Czech does not regularly omit je in normal sentences. You might see it dropped:

• In stylized language (poetry, headlines, telegram style).
• Very informally, but it is not the neutral standard.

So for everyday correct Czech, include “je”.

They are completely different words that sound the same but are written differently:

• byt (with short y) = flat, apartment
  • náš byt – our flat
• být (with long ý) = to be
  • být doma – to be at home

In your sentence:

• byt = the noun “flat”
• The verb “to be” appears as:
  • je (present)
  • byl (past)

So don’t confuse byt (a place) with být (the verb).

Very roughly using English-like hints:

• byt – [bɪt] or [bɪt̪]
  • Like English bit, but with a short, pure vowel.
• byl – [bɪl]
  • Like English bill, again short and pure.
• drahý – [ˈdraɦiː]
  • dra- like “dra” in dragon (no schwa).
  • -hý: h is voiced, like English h but a bit stronger, vowel is long ee: -hee (but no y sound).
• levný – [ˈlɛvniː]
  • lev-: lev like in “level” (first syllable), but short; clear e as in get.
  • -ný: nee with a long ee.

Stress in Czech is always on the first syllable:

• NÁŠ nový byt je DRA-hý, ale NÁŠ STA-rý byt byl LEV-ný.

Czech has no articles (no equivalents of a/an/the). The specific or generic meaning is understood from:

• Context
• Word order
• Sometimes demonstratives like ten / ta / to (“that / this”)

So:

• náš byt can mean our flat or our apartment (definite by meaning).
• If you wanted to emphasize that specific old flat, you could say:
  • ale ten starý byt byl levný – but that old flat was cheap.

But grammatically, no article is needed, because the language simply doesn’t use them.