Mobilní operátor chce prodloužit smlouvu na dobu určitou.

Because smlouvu is the accusative singular form of smlouva.

Here, smlouvu is the direct object of prodloužit: the operator wants to extend the contract, so Czech uses the accusative.

• nominative: smlouva = contract
• accusative: smlouvu = contract (as the object)

So:

• Smlouva je platná. = The contract is valid.
• Podepsal smlouvu. = He signed the contract.

For the same basic reason: the phrase uses the accusative.

The preposition na often takes the accusative, and in the expression na dobu určitou it means something like for a fixed period / for a definite term.

So both words change form:

• doba → dobu
• určitá → určitou

The adjective určitou has to agree with dobu in:

• gender: feminine
• number: singular
• case: accusative

It is a very common fixed expression meaning for a fixed term, for a definite period, or for a limited duration.

It is especially common in legal, work, and contract language. A useful opposite is:

• na dobu určitou = for a fixed term
• na dobu neurčitou = for an indefinite term / open-ended

So in this sentence, the idea is that the contract would be extended only for a defined period, not indefinitely.

Both are possible in Czech, but they do not mean exactly the same thing.

• na dobu určitou is a set legal-style phrase meaning for a fixed term
• na určitou dobu usually means for some period of time / for a certain amount of time

So the word order changes the nuance:

• na dobu určitou = fixed-term, formal, contractual
• na určitou dobu = for a certain time, more general

That is why na dobu určitou is the natural choice here.

Chce is the 3rd person singular present of chtít, which means to want.

So:

• chci = I want
• chceš = you want
• chce = he/she/it wants

In this sentence, the subject is mobilní operátor, which is singular, so the verb must also be singular:

• Mobilní operátor chce... = The mobile operator wants...

Because prodloužit is perfective, and Czech usually uses the perfective infinitive when talking about wanting to achieve a completed result.

Here the idea is:

• the operator wants to complete the extension

So chce prodloužit means wants to extend / wants to renew as a single completed action.

By contrast:

• prodlužovat is imperfective
• it suggests an ongoing, repeated, or process-like action

So:

• chce prodloužit smlouvu = wants to extend the contract
• chce prodlužovat smlouvu would sound more like wants to keep extending it / wants to be extending it, which is not the normal meaning here

Mobilní operátor is the subject of the sentence, so it is in the nominative.

That is why both words appear in their dictionary-style form:

• mobilní = mobile
• operátor = operator / carrier

The phrase does decline in other cases, for example:

• nominative: mobilní operátor
• genitive: mobilního operátora
• dative: mobilnímu operátorovi

So it is not frozen; it just happens to be in the nominative here.

Usually not in this kind of sentence.

In modern Czech, mobilní operátor usually means a mobile phone provider / carrier / network operator, that is, the company itself.

So learners should not imagine a switchboard operator here. In business or contract contexts, it normally refers to the telecom company.

Because Czech does not have articles like English a/an and the.

So mobilní operátor can mean:

• a mobile operator
• the mobile operator

The exact meaning depends on context.

The same is true for smlouvu:

• a contract
• the contract

English has to choose an article, but Czech usually leaves that information unstated unless context makes it clear.

No, Czech word order is fairly flexible because case endings show the grammatical roles.

The original sentence is a normal, neutral order:

• Mobilní operátor chce prodloužit smlouvu na dobu určitou.

But other orders are possible for emphasis, for example:

• Smlouvu chce mobilní operátor prodloužit na dobu určitou.

  • puts more emphasis on the contract

• Na dobu určitou chce mobilní operátor prodloužit smlouvu.

  • puts more emphasis on for a fixed term

So the original version is probably the most neutral and natural choice if you are just stating the fact.