Мой партнёр уже приехал.

Because партнёр is a masculine singular noun in the nominative case.

Russian possessive words like мой change to match the noun they describe:

• мой = masculine singular
• моя = feminine singular
• моё = neuter singular
• мои = plural

So:

• мой партнёр = my partner
• моя подруга = my female friend
• моё место = my seat / my place

Партнёр usually means partner, but the exact meaning depends on context. It can mean:

• a romantic partner
• a business partner
• a dance/sports partner
• sometimes just a person you work together with

So the Russian word is broad, much like English partner.

Also note the letter ё in партнёр. It is pronounced yo, and it marks the stress: партнёр.

Уже means already.

In Мой партнёр уже приехал, it modifies the verb приехал, so the meaning is My partner has already arrived.

Its position is natural and very common:

• Мой партнёр уже приехал.

Russian word order is fairly flexible, but this order sounds neutral and natural.

Because Russian does not use an auxiliary verb like English has in this kind of sentence.

Приехал is the past tense form of приехать, and because приехать is perfective, it usually expresses a completed action:

• приехал = arrived / has arrived

So one Russian word can correspond to either:

• arrived
• has arrived

The best English translation depends on context.

In Russian past tense, verbs often have an -л- element, and they also agree with the subject in gender and number.

Here the subject is партнёр, which is masculine singular, so the verb is:

• приехал = masculine singular

Compare:

• Мой партнёр приехал. = my partner arrived (male / grammatically masculine)
• Моя партнёрша приехала. = my female partner arrived
• Мои партнёры приехали. = my partners arrived

So the ending helps show who did the action.

Because Russian often omits subject pronouns when the subject is already clear.

Here, the subject is explicitly stated as Мой партнёр, so adding он would be unnecessary:

• Мой партнёр уже приехал. = natural
• Он уже приехал. = He has already arrived
• Мой партнёр, он уже приехал. = possible in special spoken contexts, but not the normal basic form

Russian often avoids repeating information that is already obvious.

The dictionary form is приехать.

This verb means to arrive by transport or to come by vehicle. For example, someone arrives:

• by car
• by train
• by bus
• by plane

So приехал often suggests arrival from somewhere else, typically by some means of transport.

This is a very common question.

• приехал = arrived/came by transport
• пришёл = came/arrived on foot

So:

• Мой партнёр уже приехал. = My partner has already arrived, probably by car/train/etc.
• Мой партнёр уже пришёл. = My partner has already come, probably on foot

Russian often makes this distinction more clearly than English does.

A helpful pronunciation guide is:

Мой партнёр уже приехал
moy part-NYOR oo-ZHE pri-YE-khal

Approximate stress:

• мой
• партнёр
• уже
• приехал

A few pronunciation notes:

• ё in партнёр is always stressed and sounds like yo
• ж in уже sounds like the s in measure
• х in приехал is like the ch in Scottish loch or German Bach

Yes, Russian word order is flexible, but different orders can sound more natural in different contexts.

The neutral version is:

• Мой партнёр уже приехал.

Other possible versions include:

• Мой партнёр приехал уже.
  This is possible, but it may sound more conversational or slightly marked.

• Уже мой партнёр приехал.
  This is much less neutral and would usually need a special context or emphasis.

So for a learner, Мой партнёр уже приехал is the best standard pattern to remember.

Grammatically, it is in the past tense because приехал is a past-tense form.

However, in meaning, it often overlaps with English present relevance, which is why English may use has arrived.

So:

• Russian grammar: past tense
• English translation: often has arrived or arrived

That is very normal with Russian perfective past verbs.