
die Freigabe
approval
Official permission or authorization to use, publish, sell, or begin something.
Der Softwareentwickler wartet auf die Freigabe des neuen Updates.
The software developer is waiting for approval of the new update.
approval / release
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approval
Official permission or authorization to use, publish, sell, or begin something.
Der Softwareentwickler wartet auf die Freigabe des neuen Updates.
The software developer is waiting for approval of the new update.

reopening / release
The lifting of a closure or blockage so that something is accessible or passable again.
Nach dem Unfall dauerte die Freigabe der Autobahn mehrere Stunden.
After the accident, the reopening of the highway took several hours.

sharing / access
In information technology, the permission that grants other users access to a file, folder, or resource in a network.
Ich habe dir den Link zur Freigabe des Dokuments geschickt.
I sent you the link for sharing the document.
'Freigabe' (approval/release) is the noun form of the verb 'freigeben' (to release/approve). It is made up of 'frei' (free) and 'Gabe' (giving) and describes the act or result of 'frei zu geben' (to release), that is, to permit something or make it accessible.
Die Freigabe der neuen Softwareversion erfolgt morgen.
The release of the new software version will take place tomorrow.
Very often, a genitive or the preposition 'für' (for) is used to specify exactly what is being approved or released. This is typical in formal and official contexts.
Die Freigabe des Budgets steht noch aus.
The approval of the budget is still pending.
In the context of permissions, 'Freigabe' (approval) is often used with the verbs 'erteilen' (to grant), 'erhalten' (to receive), or 'benötigen' (to need). These combinations are very common in professional and administrative life.
Der Projektleiter muss die Freigabe für die nächste Phase erteilen.
The project manager has to grant approval for the next phase.
When it refers to lifting a closure, you will usually find 'Freigabe' (reopening/release) in connection with traffic routes. Typical nouns are 'Autobahn' (highway), 'Straße' (road), 'Brücke' (bridge), or 'Strecke' (route/section).
Die Polizei kündigte die Freigabe der Brücke für den Abend an.
The police announced the reopening of the bridge for the evening.
In IT, 'Freigabe' (sharing/access) refers to access permission for digital resources. Signal words for this meaning are 'Datei' (file), 'Ordner' (folder), 'Netzwerk' (network), or 'Link' (link).
Kannst du mir bitte die Freigabe für diesen Ordner erteilen?
Could you please give me access to this folder?
approval / permit
Both words refer to official permission. Genehmigung is formal approval for a specific project, while Freigabe emphasizes that something may then be used, published, sold, or started. Genehmigung is more appropriate for the administrative act, and Freigabe for the subsequent use.

Nach der Prüfung erteilte der Verlag die Freigabe zur Veröffentlichung des Buches.
After the review, the publisher authorized the book for publication.
Für die Veröffentlichung des Buches erteilte die Behörde die Genehmigung.
The authorities granted approval for the book to be published.