jemandem zustehen
to be entitled
To have a right to something; to be entitled to receive or do something.
Jedem Arbeitnehmer stehen mindestens 24 Urlaubstage pro Jahr zu.
Every employee is entitled to at least 24 vacation days per year.

to be entitled / be one's place
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to be entitled
To have a right to something; to be entitled to receive or do something.
Jedem Arbeitnehmer stehen mindestens 24 Urlaubstage pro Jahr zu.
Every employee is entitled to at least 24 vacation days per year.

'Zustehen' is a separable verb. The prefix 'zu' separates in main clauses and goes to the end. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Diese Pause steht Ihnen gesetzlich zu.
You are legally entitled to this break.
This verb is always used with the dative. The person who has a right to something or about whom a judgment is being made is in the dative (wem?). The thing that is due or appropriate is the subject of the sentence.
Dem Kunden steht eine Rückerstattung zu.
The customer is entitled to a refund.
In this meaning, 'zustehen' is often combined with legal or formal claims. Typical phrases are: 'ein Recht steht jemandem zu' (someone is entitled to a right), 'Urlaubstage stehen zu' (vacation days are due), 'eine Entschädigung steht zu' (compensation is due), or 'ein Anteil steht zu' (a share is due).
Nach dem Gesetz steht Ihnen eine Abfindung zu.
Under the law, you are entitled to severance pay.
The meaning 'ein Recht haben' (to have a right) is often positive or neutral and refers to claims or entitlements. The meaning 'angemessen sein' (to be appropriate), by contrast, is often phrased negatively ('es steht dir nicht zu' — it is not your place) and refers to judgments, criticism, or behavior.
Mir steht noch ein Urlaubstag zu.
I still have one vacation day due to me.
The meaning 'etwas zugeben' (to admit something) is archaic and is hardly used in modern language anymore. You mainly find it in older literature.
Er stand seinen Irrtum schließlich zu.
He finally admitted his error.
to earn / deserve
'verdienen' and 'zustehen' can both express that someone should receive something. The difference lies in the reason for it. You use 'verdienen' when someone gains a right to something through achievement, behavior, or effort. 'zustehen' sounds more neutral and means: someone has a right to something, for example because of a rule, a role, or a position. Learners may confuse the words because both have to do with entitlement. As a practical rule: for personal achievement, 'verdienen' often fits; for a fixed right, 'zustehen' is more likely to fit.

Nach dem Vertrag stehen dir dreißig Tage Urlaub im Jahr zu.
According to the contract, you are entitled to thirty days of vacation per year.
Nach der langen Woche hat das Team eine Pause verdient.
After the long week, the team deserves a break.