Poslije trčanja uzela je gutljaj vode i još jedan mali zalogaj jabuke.

Because poslije requires the genitive case.

• trčanje = running
• genitive singular: trčanja

So:

• poslije trčanja = after running

This is very common in Croatian: certain prepositions always require a specific case, and poslije takes the genitive.

It is a verbal noun used like a regular noun.

• trčati = to run
• trčanje = running
• trčanja = genitive singular of trčanje

So poslije trčanja literally means after running, where running behaves grammatically like a noun.

This is similar to English running in after running, although the Croatian grammar behind it is different.

Uzela je is the past tense.

It is made from:

• uzela = the l-participle form
• je = the auxiliary verb is, used to build the past tense

Together:

• uzela je = she took

This is the standard Croatian perfect tense.

We know from uzela.

The participle agrees with the subject in gender and number:

• uzeo je = he took
• uzela je = she took
• uzelo je = it took
• uzeli su = they took (masculine/mixed)
• uzele su = they took (feminine)

So uzela je clearly tells us the subject is feminine singular: she.

In Croatian, the auxiliary je is a clitic, and clitics usually go in the second position of the clause.

That is why Croatian word order can look unusual to English speakers.

In this sentence:

• Poslije trčanja | uzela je | gutljaj vode...

The auxiliary stays attached in the normal clitic position after the first stressed element of its clause.

You may also hear different word orders in real speech, but uzela je is completely normal and standard here.

Gutljaj vode means a sip of water or a swallow of water.

• gutljaj = sip, swallow
• voda = water
• vode = genitive singular

After words that express an amount, portion, or unit, Croatian often uses the genitive:

• čaša vode = a glass of water
• boca vina = a bottle of wine
• gutljaj vode = a sip of water

So vode is in the genitive because it means some water / a quantity of water.

For the same reason as gutljaj vode.

• zalogaj = bite, morsel
• jabuka = apple
• jabuke = genitive singular

So:

• zalogaj jabuke = a bite of apple

Croatian commonly uses the genitive after nouns that describe a part, portion, or amount of something.

Još jedan means another or one more.

Word by word:

• još = still, yet, more
• jedan = one

Together in this sentence:

• još jedan mali zalogaj jabuke = another small bite of apple

It is a very common way to say another one in Croatian.

Examples:

• Još jednu kavu, molim. = One more coffee, please.
• Hoću još jedan komad. = I want another piece.

Because they all describe a masculine singular noun: zalogaj.

• jedan = masculine singular
• mali = masculine singular
• zalogaj = masculine singular noun

They must agree in gender, number, and case.

If the noun changed, the forms would change too. For example:

• jedna mala jabuka = one small apple
  (feminine singular)

So in još jedan mali zalogaj, everything is matching zalogaj.

They refer to different kinds of small amounts of food or drink:

• gutljaj = sip, swallow → used for liquids
• zalogaj = bite, morsel → used for food

So:

• gutljaj vode = a sip of water
• zalogaj jabuke = a bite of apple

This contrast is very natural in Croatian.

Uzeti literally means to take, but Croatian often uses it in situations where English might prefer a more specific verb.

So uzela je gutljaj vode is natural and means something like:

• she took a sip of water

Likewise:

• uzeti zalogaj = to take a bite

You could sometimes use more specific verbs in other contexts, but this sentence is perfectly idiomatic.

No. A common alternative is nakon.

Both can mean after:

• Poslije trčanja...
• Nakon trčanja...

Both take the genitive.
In everyday usage, poslije is very common and sounds natural.

Because Croatian does not have articles like English a/an/the.

So Croatian simply says:

• gutljaj vode
• mali zalogaj jabuke

and the exact English choice (a sip, the sip, a small bite, etc.) depends on context.

That is why learners often have to get used to reading Croatian nouns without articles.

Here it is genitive singular.

• nominative singular: jabuka = apple
• genitive singular: jabuke

So zalogaj jabuke means a bite of apple, not a bite of apples.

This form can be confusing because jabuke can also be nominative plural in other contexts. You have to tell from the grammar around it.

Here, after zalogaj, it is clearly genitive singular.

Yes. Uzeti is perfective.

That means it presents the action as a completed whole:

• uzeti = to take (completed act)
• uzimati = to be taking / to take repeatedly or habitually (imperfective)

In this sentence, the speaker is talking about completed actions after running, so uzela je is the natural choice.