صمام الإطار قديم، إذن يشتري المشتري صمام إطار جديدا.

In present-tense Arabic, the verb to be is usually omitted in simple statements.

So:

• صمام الإطار قديم
• literally: the tire valve old
• natural English: The tire valve is old

This kind of sentence is called a nominal sentence in Arabic.

If you wanted past or future, Arabic would usually use an actual verb such as كان:

• كان صمام الإطار قديمًا = The tire valve was old

This is an iḍāfa construction, often translated as X of Y.

• صمام الإطار
• literally: valve of the tire
• naturally: the tire valve

In an iḍāfa:

• the first noun usually does not take ال
• the first noun also does not take tanwīn
• the second noun determines whether the whole phrase is definite or indefinite

So:

• صمامُ الإطارِ = the valve of the tire = the tire valve

Even though صمام has no ال, the whole phrase is definite because الإطار is definite.

Because the two phrases are not equally definite.

1. صمام الإطار
   = the tire valve
   Here the tire is specific/definite, so you get الإطار.

2. صمام إطار جديدا
   = a new tire valve / literally a new valve of a tire
   Here the object is indefinite, so إطار is also indefinite.

So the difference reflects the difference between:

• the tire valve
  and
• a new tire valve

This is very normal in Arabic iḍāfa.

إذن means something like:

• then
• so
• therefore

In this sentence, it links the two ideas:

• The tire valve is old
• so / therefore the buyer buys a new tire valve

So it is acting as a logical connector.

In modern writing, learners will also often see other connectors used in similar contexts, such as:

• لذلك = therefore
• فـ = so
• لذا = thus / so

Good question. In traditional grammar, إذن can put a following present-tense verb into the subjunctive under certain conditions.

However, in real modern usage:

• إذن is often just used as a connector meaning so / then
• in unvoweled text, the spelling of the verb may not visibly change anyway
• many writers do not focus on the classical governing behavior unless the context is very formal or carefully vocalized

Also, with a verb like يشتري, the spelling often looks the same in normal writing even when the final vowel changes.

So for a learner, the safest takeaway is:

• here إذن mainly means so / therefore
• يشتري is simply the following verb: buys

Because Arabic very often uses verb–subject–object order.

So:

• يشتري المشتري صمامَ إطارٍ جديدًا
• literally: buys the buyer a new tire valve
• natural English: the buyer buys a new tire valve

This word order is completely normal in Arabic.

You could also say:

• المشتري يشتري صمامَ إطارٍ جديدًا

That puts the subject first and gives a bit more emphasis to the buyer.

المشتري means the buyer.

The ال makes it definite, so it refers to a specific buyer already understood from context.

Compare:

• مشتري = a buyer
• المشتري = the buyer

Also, المشتري is originally an active participle from the verb اشترى (to buy), but in practice it often functions like an ordinary noun meaning buyer.

جديدا is the adjective describing صمام.

It is:

• masculine singular
• indefinite
• accusative

Why accusative? Because صمام is the direct object of يشتري, and the adjective follows the noun it describes.

So the fully vocalized form is:

• صمامَ إطارٍ جديدًا

The final -ًا is the usual spelling of fatḥatayn on many indefinite accusative nouns/adjectives.

Why no ال?

Because the noun it describes is indefinite:

• صمام = a valve
• so the adjective must also be indefinite:
• جديدًا = new

Arabic adjectives match the noun in:

• definiteness
• gender
• number
• case

Because قديم and جديدا have different grammatical roles.

In the first clause:

• صمام الإطار قديم
• قديم is the predicate of a nominal sentence
• so it is nominative
• fully vocalized: قديمٌ

In the second clause:

• صمامَ إطارٍ جديدًا
• جديدًا describes the direct object
• so it is accusative

So the contrast is:

• قديمٌ = nominative predicate
• جديدًا = accusative adjective modifying an object

Without short vowels, Arabic script often hides this difference, but the grammar is still there.

By itself, يشتري is a present-tense/imperfect verb, so depending on context it can mean:

• buys
• is buying
• sometimes a near-future sense

In this sentence, the most straightforward reading is buys.

If you wanted to make the future very explicit, Arabic would often say:

• سيشتري = will buy
• سوف يشتري = will buy

So if the intended meaning is strongly future, many learners would expect something like:

• إذن سيشتري المشتري...

The sentence is understandable and useful for study, especially for:

• iḍāfa
• nominal sentences
• adjective agreement
• word order

But a native speaker might choose a slightly smoother version, depending on context. For example:

• صمامُ الإطارِ قديمٌ، لذلك يشتري المشتري صمامًا جديدًا للإطار.
• The tire valve is old, so the buyer buys a new valve for the tire.

Or, if the meaning is future:

• صمامُ الإطارِ قديمٌ، لذا سيشتري المشتري صمامًا جديدًا للإطار.
• The tire valve is old, so the buyer will buy a new valve for the tire.

So the original is grammatically helpful, even if there are other ways to phrase it more naturally.