Čím později přijedeme do centra, tím méně lidí bude na náměstí.

It is a very common Czech pattern meaning the more/less ..., the more/less ... or the X-er ..., the Y-er ....

So:

• Čím později přijedeme do centra, tím méně lidí bude na náměstí.
• literally: By how much later we arrive in the center, by that much fewer people will be on the square
• natural English: The later we arrive downtown, the fewer people will be in the square.

This structure is used with comparatives:

• Čím víc studuješ, tím víc umíš. = The more you study, the more you know.
• Čím dřív přijdeš, tím líp. = The earlier you come, the better.

In this pattern, čím is a fixed part of the construction čím ..., tím ....

Historically, it is the instrumental form of co. In modern Czech, learners usually just learn the whole pattern as one unit:

• čím ...
• tím ...

You do not need to analyze it every time while speaking. It is best memorized as a set phrase meaning the ... the ....

Později is the comparative adverb of pozdě.

• pozdě = late
• později = later

Since the sentence compares one situation with another, Czech uses the comparative:

• Čím později... = The later...

Compare:

• brzy → dřív / dříve = early → earlier
• hodně → víc / více = much/a lot → more
• málo → méně = little/few → less/fewer

Přijedeme is from the verb přijet, which is perfective. In Czech, the present-tense form of a perfective verb usually has future meaning.

So:

• přijedeme = we will arrive

This is normal Czech grammar, not a special exception.

Compare:

• jedeme from jet (imperfective) = we are going / we go
• přijedeme from přijet (perfective) = we will arrive

Czech does not say budeme přijet.

The preposition do takes the genitive case and usually means into, to, inside, to the area of.

So:

• centrum = center, downtown, city center
• genitive singular = centra
• do centra = to the center / downtown

This is standard:

• do města = to the city
• do školy = to school
• do domu = into the house

In everyday Czech, centrum very often means the city center / downtown, not just a geometric center.

So do centra in this sentence would normally be understood as:

• to the city center
• downtown

depending on context and the English style you want.

After expressions of quantity like méně, Czech usually uses the genitive.

So:

• lidé = people (nominative plural)
• lidí = people (genitive plural)

Therefore:

• méně lidí = fewer people

This is very common after quantity words:

• hodně lidí = a lot of people
• málo času = little time
• několik studentů = several students

This is a very common point for learners.

In méně lidí bude na náměstí, the verb is often singular because the quantity expression méně lidí is treated as a kind of amount.

So Czech commonly says:

• bude méně lidí = there will be fewer people

This is similar to:

• Je tam hodně lidí. = There are a lot of people there.
• Bylo tam málo hostů. = There were few guests there.

In modern usage, quantity expressions often lead to singular neuter-style agreement or a singular verb in existential sentences like this. For a learner, the safest thing is simply to remember:

• bude méně lidí
• bylo hodně lidí
• je málo času

Czech uses na with some places where English uses in or at.

With náměstí = square, the normal expression is:

• na náměstí = in the square / on the square / at the square

This is just the standard collocation in Czech.

Other common place expressions with na:

• na ulici = on the street / in the street
• na zastávce = at the stop
• na nádraží = at the station

Here na náměstí is in the locative case, and the form of náměstí happens to stay the same.

The comma separates the two halves of the correlative structure:

• Čím později přijedeme do centra, tím méně lidí bude na náměstí.

This is standard Czech punctuation for this kind of sentence, just like English often separates the two parts of the more..., the more... constructions.

Yes, Czech word order is fairly flexible, but this structure normally stays clearly in two parts:

• Čím později přijedeme do centra, tím méně lidí bude na náměstí.

You may sometimes see small shifts for emphasis, but čím ... tím ... should remain easy to recognize.

For learners, the best approach is to keep the standard order until it feels natural.

In standard Czech, později is the normal form here.

You may also hear colloquial variants in speech in some regions, but for neutral, standard Czech:

• pozdě = late
• později = later

So this sentence is perfectly standard and natural as written.

You could use that to understand the grammar, but it is not natural English. The best natural translation is:

• The later we arrive downtown, the fewer people will be in the square.

A more literal internal gloss can help you learn the Czech structure, but for real translation, use the normal English the ... the ... pattern.