Veterinar ima vakcinu i sutra će vakcinisati psa.

Serbian does not use articles the way English does. So veterinar can mean the veterinarian, a veterinarian, or just veterinarian, depending on context. The same is true for vakcinu and psa.

In this sentence, English would usually translate it with the: The veterinarian has the vaccine and will vaccinate the dog tomorrow, but Serbian leaves that unstated.

Veterinar is in the nominative singular, because it is the subject of the sentence: the veterinarian is the one doing the actions.

The two actions are:

• ima = has
• će vakcinisati = will vaccinate

So veterinar is the subject for both verbs.

Ima is the 3rd person singular present tense of imati = to have.

So veterinar ima vakcinu means the veterinarian has the vaccine.

There is no separate word for he or she because Serbian often omits subject pronouns when the subject is already clear. Here, the noun veterinar already tells us who is doing the action, so adding on would be unnecessary.

Because vakcinu is the accusative singular form of vakcina.

Here, vakcina is the direct object of ima: it is the thing that the veterinarian has.

For most feminine nouns ending in -a, the accusative singular ends in -u:

• vakcina → vakcinu
• knjiga → knjigu
• mačka → mačku

So:

• vakcina = nominative
• vakcinu = accusative

Because psa is the accusative singular of pas, and pas is a masculine animate noun.

In Serbian, masculine animate nouns usually have:

• nominative: pas
• accusative: psa

This is very important: for masculine animate nouns, the accusative usually looks like the genitive.

Compare:

• Vidim psa. = I see the dog.
• Imam psa. = I have a dog.

But with a masculine inanimate noun, the accusative is usually the same as the nominative.

This is the future tense in Serbian.

A common way to form it is:

• će
  • infinitive

So:

• će vakcinisati = will vaccinate

In this sentence:

• sutra će vakcinisati psa = tomorrow [he/she] will vaccinate the dog

The word će is a short future auxiliary, related to the verb hteti = to want.

Yes. In many cases, Serbian can express this future in a joined form:

• će vakcinisati
• vakcinisaće

Both mean will vaccinate.

So these are both possible:

• Sutra će vakcinisati psa.
• Sutra vakcinisaće psa. is not the usual word order.
• Vakcinisaće psa sutra. is possible.
• Veterinar će sutra vakcinisati psa. is also possible.

The safest standard pattern for learners is usually će + infinitive, as in your sentence.

Because će is a clitic, a short unstressed word that usually appears in the second position of its clause.

In sutra će vakcinisati psa:

• sutra is the first element
• će comes second

That is why Sutra će vakcinisati psa sounds natural.

You can also rearrange the sentence, for example:

• Veterinar će sutra vakcinisati psa.
• Sutra će veterinar vakcinisati psa.

Serbian word order is fairly flexible, but clitics like će have placement rules.

Here i simply means and, joining two parts that share the same subject:

• Veterinar ima vakcinu
• (Veterinar) sutra će vakcinisati psa

The second veterinar is not repeated because it is already understood. English does the same thing:

• The veterinarian has the vaccine and will vaccinate the dog tomorrow.

Yes. Sutra means tomorrow, and Serbian allows some movement of adverbs like this.

Possible versions include:

• Veterinar ima vakcinu i sutra će vakcinisati psa.
• Veterinar ima vakcinu i će sutra vakcinisati psa. → not correct, because of clitic placement
• Veterinar ima vakcinu i veterinar će sutra vakcinisati psa. → grammatical, but repetitive
• Veterinar će sutra vakcinisati psa.
• Sutra će veterinar vakcinisati psa.

Changing the position can slightly change emphasis, but the basic meaning stays the same.