Vreau încă un pahar cu apă rece.

Romanian often drops subject pronouns because the verb ending already shows who is doing the action.

• vreau = I want
• vrei = you want
• vrea = he/she wants

So Vreau încă un pahar cu apă rece is a complete sentence. You could say Eu vreau..., but that adds emphasis, like I want....

Here, încă means another or one more.

So:

• încă un pahar = another glass / one more glass

Be careful: încă can also mean still in other contexts.

• Încă aștept. = I am still waiting.

In this sentence, because it comes before un pahar, it clearly means another / one more.

Romanian usually expresses another glass as one more glass, so încă un pahar is very natural.

Literally, it is:

• încă = more / another
• un = a / one
• pahar = glass

English often says just another glass, but Romanian normally keeps un with a singular countable noun.

Because pahar is a neuter noun in Romanian.

Neuter nouns behave:

• like masculine in the singular
• like feminine in the plural

So:

• singular: un pahar
• plural: două pahare

That is why the singular article is un, not o.

Both un pahar cu apă and un pahar de apă can be natural, but they are slightly different in feel.

• un pahar cu apă = a glass with water in it
• un pahar de apă = a glass of water

In everyday speech, both are common. In this sentence, cu apă rece sounds very natural because the phrase is describing the contents of the glass: with cold water.

It describes apă.

So the meaning is:

• a glass with cold water

not

• a cold glass with water

Romanian usually places the adjective after the noun it describes, and here rece follows apă, so it naturally goes with apă.

In Romanian, adjectives usually come after the noun.

So:

• apă rece = cold water
• pahar mare = big glass
• mașină nouă = new car

Romanian can sometimes put adjectives before the noun, but that is less neutral and often adds emphasis or a stylistic effect. In this sentence, apă rece is the normal word order.

It actually is agreeing with apă, but rece has the same singular form for both masculine and feminine.

Compare:

• apă rece = cold water
• ceai rece = cold tea

But in the plural it changes:

• ape reci = cold waters
• ceaiuri reci = cold teas

So the agreement is there; it just is not very visible in the singular.

It is understandable, but it can sound fairly direct.

More polite options are:

• Aș vrea încă un pahar cu apă rece, vă rog. = I would like another glass of cold water, please.
• Îmi mai aduceți un pahar cu apă rece, vă rog? = Could you bring me another glass of cold water, please?

If you do use Vreau..., adding vă rog helps:

• Vreau încă un pahar cu apă rece, vă rog.

Sometimes yes, but they are not always identical.

• Mai vreau un pahar cu apă rece. = I want another glass of cold water / I want one more glass of cold water.
• Vreau încă un pahar cu apă rece. = also I want another glass of cold water.

In requests like this, both can work. încă directly modifies the noun phrase un pahar, while mai often has a broader meaning of more / again / another one in the sentence. Learners will hear both in real Romanian.