Если у кошки снова пропадёт аппетит, лучше отвезти её к ветеринару.

Because Russian often uses у + genitive to mean with, in, or as for someone when talking about states or conditions.

So у кошки снова пропадёт аппетит literally feels like:

At the cat / in the cat’s case, the appetite will disappear again.

This is a very natural Russian pattern for things like:

• У меня болит голова — I have a headache
• У ребёнка температура — The child has a fever
• У кошки пропал аппетит — The cat lost its appetite

Here, кошки is the genitive singular of кошка.

Because аппетит is the grammatical subject of пропадёт.

Russian structures this idea as:

аппетит пропадёт — the appetite will disappear

So even though English says the cat loses its appetite, Russian is literally saying something closer to:

the appetite will disappear in the cat / for the cat

That is why:

• аппетит = nominative subject
• у кошки = a kind of possessor/experiencer phrase

Пропадёт is future tense of the perfective verb пропасть.

It is used because the sentence is talking about a possible future event:

If the cat loses its appetite again...

Compare:

• пропадает — is disappearing / disappears regularly / is in the process of disappearing
• пропадёт — will disappear, will be lost

In an если clause about a future possibility, Russian normally uses the future, not the present:

• Если он придёт... — If he comes...
• Если у кошки снова пропадёт аппетит... — If the cat loses its appetite again...

Even though English uses present tense after if, Russian uses future here.

Here it means to disappear, and in context, to go away or to be lost.

So пропадёт аппетит means:

• the appetite will disappear
• the cat will lose its appetite

This is a very normal Russian way to express loss of appetite.

You may also see the past tense:

• У кошки пропал аппетит — The cat lost its appetite

Снова means again.

Its position before the verb is very natural and emphasizes the repeated event:

Если у кошки снова пропадёт аппетит... = If the cat loses its appetite again...

Russian word order is more flexible than English, but this placement is the most neutral here.

You could move снова in some contexts, but the original sentence sounds standard and natural.

Лучше + infinitive is a very common Russian way to give advice:

• Лучше подождать — It’s better to wait
• Лучше не спорить — Better not argue
• Лучше отвезти её к ветеринару — It’s better to take her to the vet

It sounds like a recommendation, not a strict obligation.

Compare:

• лучше отвезти — it would be better to take her
• нужно отвезти — it is necessary to take her
• надо отвезти — need to take her / should take her

So лучше makes the sentence sound like practical advice.

Отвезти is a perfective infinitive meaning to take/drive someone somewhere by transport, with focus on the completed trip.

Important contrasts:

• везти — to be transporting by vehicle, imperfective
• отвезти — to take/drive someone somewhere, perfective
• вести — to lead/take on foot
• отвести — to take someone somewhere on foot, perfective

So:

• отвезти её к ветеринару suggests taking the cat there by car, taxi, carrier, etc.
• If you were talking about walking a person somewhere, you would more likely use отвести

The perfective отвезти fits well because this is a single recommended action: get the cat to the vet.

Because её is the accusative form of она.

The cat is the object of отвезти:

• отвезти кого? — to take whom?
• её — her

So:

• она = she
• её = her

Since кошка is feminine, the pronoun is feminine too.

Ветеринару is dative singular.

That is because the preposition к takes the dative when it means to / toward a person or place.

So:

• к кому? — to whom?
• к ветеринару — to the veterinarian

Other examples:

• к врачу — to the doctor
• к другу — to a friend
• к маме — to mom

So in the sentence:

отвезти её к ветеринару = to take her to the veterinarian

Russian often leaves the subject unstated in general advice.

Лучше отвезти её к ветеринару literally means something like:

It’s better to take her to the vet

The sentence does not explicitly say you, but that is understood from context. English often needs a subject, while Russian can be more impersonal.

So the idea is:

• If the cat loses its appetite again, it would be better to take her to the vet.

The understood person is whoever is responsible for the cat.

Because Если у кошки снова пропадёт аппетит is a subordinate clause introduced by если.

Russian, like English, normally separates this kind of if-clause with a comma:

• Если будет дождь, мы останемся дома.
• Если у кошки снова пропадёт аппетит, лучше отвезти её к ветеринару.

So the comma marks the boundary between:

1. the condition
2. the main clause

More or less, yes:

Если — if
у кошки — in the cat / with the cat / the cat’s
снова — again
пропадёт — will disappear
аппетит — appetite
лучше — better
отвезти — to take/drive
её — her
к ветеринару — to the veterinarian

A very literal version would be:

If the cat’s appetite disappears again, it is better to take her to the veterinarian.

A more natural English translation is:

If the cat loses its appetite again, it’s best to take her to the vet.

Ветеринар means veterinarian, but in many contexts it works like English vet too.

So:

• к ветеринару can mean to the veterinarian
• in normal conversation, it is often best translated as to the vet

Russian does also use the shorter colloquial form ветеринарка for a vet clinic in some contexts, but here ветеринару clearly means the person.

Because кошка is a grammatically feminine noun, and it specifically means a female cat.

So Russian naturally uses the feminine pronoun:

• кошка — female cat
• её — her

If it were a male cat, you would usually say кот and then use его.

That said, in English people sometimes say its for animals, but Russian more often uses personal pronouns when talking about animals, especially pets.