Sykepleieren ber de pårørende vente i et stille rom.

Norwegian often marks definiteness with a suffix on the noun.

• sykepleier = a nurse (indefinite)
• sykepleieren = the nurse (definite)
  The ending -en is the common definite ending for many masculine nouns in Bokmål.

ber is the present tense of å be (to ask/request), and it often implies a request/instruction.

• å be = ask/request someone to do something (can sound more formal/authority-based)
• å spørre = ask a question / inquire
  So Sykepleieren ber ... fits when the nurse is requesting/directing someone.

Here de is a determiner meaning the (definite plural), not the subject pronoun they.

• de pårørende = the relatives / the next of kin
  The pronoun de (they) would typically be used without a noun after it.

pårørende is originally an adjective/participle meaning roughly related/connected, but in modern Norwegian it’s very commonly used as a noun meaning relatives / next of kin (especially in medical contexts).
So de pårørende functions like a normal noun phrase: the next of kin.

After å be, Norwegian often uses a bare infinitive (without å) when you have be + someone + infinitive:

• å be noen vente = to ask someone to wait

You can also use an alternative structure with om:

• å be noen om å vente (also correct; can feel slightly more “request-like”/polite or a bit more explicit)

vente is the infinitive (to wait). In this structure, it’s the action the relatives are being asked to do. It does not show tense itself; the tense is carried by ber (present tense).

Because you wait inside a room, Norwegian uses i (in).

• i et rom = in a room
  på is used more for on a surface or in certain set location types (e.g., på sykehuset = at/in the hospital as an institution), but for a physical room, i is the normal choice.

et is the indefinite article for neuter nouns.

• et rom = a room (neuter)
  If it were a common gender noun, you’d expect en (e.g., en stol).

Many adjectives have a special neuter ending -t (e.g., en fin bil / et fint hus).
But adjectives ending in -e like stille usually don’t add -t in neuter:

• en stille person / et stille rom

If it were definite, you’d typically get the weak form (still stille):

• det stille rommet = the quiet room

It’s standard main-clause Norwegian word order (similar to English here):

• Subject: Sykepleieren
• Verb: ber
• Object: de pårørende
• Infinitive complement: vente
• Place phrase: i et stille rom

If you moved the place phrase to the front, Norwegian would use V2 word order (verb still second):

• I et stille rom ber sykepleieren de pårørende vente.