Поставщик услуг пересчитает задолженность при условии, что претензия принята.

Пересчитает is the future tense of the perfective verb пересчитать.

Here it means will recalculate / will recalculate once. The perfective aspect is used because the sentence refers to a completed result: the service provider will perform one finished action if the condition is met.

Compare:

• пересчитает = will recalculate as a completed action
• будет пересчитывать = will be recalculating / will recalculate repeatedly or as a process

In formal notices like this, the perfective future is very common.

Поставщик means supplier or provider.
The noun that follows it, услуг, is in the genitive plural.

So:

• поставщик = provider/supplier
• услуг = of services

Literally, поставщик услуг means provider of services, which English usually renders as service provider.

This noun + genitive pattern is very common in Russian:

• производитель товаров = manufacturer of goods
• поставщик воды = supplier of water
• поставщик услуг = provider of services

Because поставщик typically takes the genitive for the thing being supplied or provided.

The dictionary form is:

• услуга = service

Its genitive plural is:

• услуг

So поставщик услуг literally means provider of services.

Russian often uses the plural here even where English may prefer a more general singular-like translation.

Задолженность is in the accusative singular, because it is the direct object of пересчитает.

The service provider will recalculate what?
→ задолженность

But the form looks the same as the nominative because:

• it is an inanimate feminine noun
• many feminine nouns of this type have the same nominative and accusative form

So:

• nominative: задолженность
• accusative: задолженность

This is normal.

Задолженность is a formal word meaning something like:

• debt
• outstanding balance
• amount owed
• arrears

In billing, utilities, and other official contexts, задолженность is more formal and technical than долг.

So in this sentence it likely means the customer’s outstanding amount due will be recalculated.

При условии, что is a formal conjunction meaning:

• provided that
• on condition that
• as long as

It introduces the condition under which the main action will happen.

So the structure is:

• Поставщик услуг пересчитает задолженность = the provider will recalculate the debt
• при условии, что претензия принята = provided that the claim has been accepted / is accepted

This expression is common in formal, legal, and administrative Russian.

Because что introduces a subordinate clause.

In при условии, что, the comma is standard:

• при условии, что претензия принята

This is similar to other formal patterns such as:

• в случае, если...
• при том, что...

So the comma is required by normal Russian punctuation.

Претензия is more formal and often used in business, legal, and consumer-rights contexts.

It usually means a formal claim, complaint, or demand submitted to a company or institution.

By contrast:

• жалоба = a general complaint
• претензия = a more official claim/complaint, often one that can lead to a formal review or correction

In a sentence about recalculating a debt, претензия sounds exactly like the kind of official word Russian would use.

Because принята is a short passive participle from принять.

So:

• претензия принята = the claim is accepted / the claim has been accepted

This is very common in formal and bureaucratic Russian. It sounds concise, impersonal, and official.

A more verb-based paraphrase would be:

• если претензию приняли

But the original version is more typical of administrative style.

Because short passive participles agree with the noun in gender and number.

Here the noun is:

• претензия — feminine singular

So the participle must also be feminine singular:

• принята

Compare:

• документ принят = the document is accepted
• заявление принято = the application is accepted
• претензия принята = the claim is accepted
• документы приняты = the documents are accepted

Russian often omits the equivalent of is in the present tense, and short passive participles can describe a resulting state very compactly.

So претензия принята can mean:

• the claim is accepted
• the claim has been accepted

depending on context.

If Russian wanted to make it more explicitly past, it could say:

• претензия была принята

But in official language, the shorter version is extremely common.

The word order here is the most neutral and formal one:

• Поставщик услуг — subject
• пересчитает — verb
• задолженность — object
• при условии, что... — condition

Russian word order is flexible, so parts could be moved for emphasis. But in legal or administrative writing, this straightforward order is the most natural.

It reads like a typical official statement.

Yes. Very much so.

Several things make it sound formal:

• поставщик услуг instead of a simpler everyday subject
• задолженность instead of the more basic долг
• при условии, что instead of a more everyday если
• претензия принята with a short passive participle

Altogether, this sounds like something from:

• a utility company notice
• a contract
• billing rules
• a consumer-rights document