Μετά τη γέφυρα ο δρόμος στενεύει, γι’ αυτό πρέπει να προσέχεις.

Here it is about place, not time.

Μετά τη γέφυρα means after the bridge, past the bridge, or once you go beyond the bridge. In other words, the road becomes narrower at the point after you pass the bridge.

Because μετά takes the accusative in Modern Greek when it means after.

So:

• η γέφυρα = the bridge (nominative)
• τη γέφυρα = the bridge (accusative)

After μετά, you use the accusative form:

• μετά τη γέφυρα

The feminine article την often loses its final -ν before certain consonants. Since γέφυρα begins with γ, it is very normal to say and write τη γέφυρα.

So:

• τη γέφυρα = the usual form here
• την γέφυρα may be heard or seen sometimes, but τη γέφυρα is the standard everyday choice in this sentence

Greek uses the definite article very often, more regularly than English in many contexts.

Here ο δρόμος means the road. It refers to the specific road being talked about, so the article is natural.

• ο δρόμος = the road
• δρόμος by itself would be more like road as a dictionary form or a less complete phrase

Στενεύει comes from στενεύω, which means to become narrow or to narrow.

So ο δρόμος στενεύει means:

• the road narrows
• the road gets narrower

It is a very natural verb for roads, streets, passages, clothes, spaces, and so on.

It is the third person singular present tense form of στενεύω.

So:

• στενεύω = I narrow / I become narrow
• στενεύεις = you narrow / you become narrow
• στενεύει = he, she, it narrows / becomes narrow

Since the subject is ο δρόμος (the road), Greek uses στενεύει.

Γι’ αυτό means therefore, that’s why, or for this reason.

It is a shortened form of για αυτό, with the α of για dropped in pronunciation and spelling. The apostrophe shows that something has been omitted:

• για αυτό → γι’ αυτό

In this sentence, it connects the two ideas:

• the road narrows
• therefore you need to be careful

This is a very useful Greek aspect question.

• πρέπει να προσέχεις uses the present/imperfective form
• πρέπει να προσέξεις uses the aorist/perfective form

Here, πρέπει να προσέχεις means you should be careful / you need to keep paying attention. It suggests ongoing caution, not just one single moment.

That fits the situation well: after the bridge, the road is narrower, so you need to stay alert.

By contrast, πρέπει να προσέξεις would sound more like:

• you must be careful
• watch out

It can work too in some contexts, but προσέχεις emphasizes a more continuous state of caution.

Because Greek usually does not need a subject pronoun when the verb ending already shows the subject.

The ending -εις in προσέχεις tells you it means you singular.

So Greek can simply say:

• πρέπει να προσέχεις = you must be careful

If you add εσύ, it gives extra emphasis:

• γι’ αυτό εσύ πρέπει να προσέχεις = that’s why you must be careful

But in a neutral sentence, Greek normally leaves εσύ out.

The word order here is the most natural neutral order:

• Μετά τη γέφυρα ο δρόμος στενεύει, γι’ αυτό πρέπει να προσέχεις.

Greek word order is fairly flexible, so some parts could move for emphasis. For example, you might also hear:

• Μετά τη γέφυρα στενεύει ο δρόμος...

But the original version is clearer and more standard for ordinary directions or warnings.

So yes, Greek word order can change, but this sentence is already in a very natural form.