der Austritt
withdrawal
Leaving an organization, club, party, or religious community.
Er hat seinen Austritt aus dem Sportverein schriftlich erklärt.
He declared his withdrawal from the sports club in writing.

withdrawal / leak / balcony
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withdrawal
Leaving an organization, club, party, or religious community.
Er hat seinen Austritt aus dem Sportverein schriftlich erklärt.
He declared his withdrawal from the sports club in writing.

'Der Austritt' (withdrawal/leak/small balcony) is the noun related to the separable verb 'austreten' (to step out, to leave). The basic idea of 'stepping outside' connects all meanings: 'stepping out' of an organization, 'coming out' of a container (leaking), or stepping out onto a balcony.
Wegen des hohen Beitrags will er aus dem Verein austreten.
Because of the high membership fee, he wants to leave the club.
The preposition helps distinguish the meanings. 'Der Austritt aus' + dative describes leaving an organization. 'Der Austritt von' + dative describes the escape of a substance.
Sein Austritt aus der Partei sorgte für Aufsehen.
His withdrawal from the party caused a stir.
When leaving an organization, people often speak of 'seinen Austritt erklären' (to declare one's withdrawal), 'einreichen' (to submit), or 'bekannt geben' (to announce). Common contexts are 'der Austritt aus der Kirche' (leaving the church) or 'aus einer Partei' (from a party).
Sie hat ihren Austritt aus dem Vorstand offiziell erklärt.
She officially declared her withdrawal from the board.
When substances escape, typical combinations are 'der Austritt von Gas/Öl/Wasser' (the leak of gas/oil/water) or 'ein unkontrollierter Austritt' (an uncontrolled leak). The goal is often to 'einen Austritt verhindern' (prevent a leak) or 'zu stoppen' (stop it).
Die Feuerwehr konnte den Austritt der Chemikalien schnell stoppen.
The fire department was able to stop the chemical leak quickly.
admission / entry
'der Eintritt' and 'der Austritt' are connected with membership in an organization, but they show opposite directions. 'Eintritt' here means that someone becomes a member or goes in. 'Austritt' means that someone leaves an organization, club, or party. The words can be confused because both often appear in formal texts about clubs or groups. The direction is important: 'Eintritt' means going in or becoming a member; 'Austritt' means going out or ending membership.

Sein Austritt aus der Partei wurde gestern bekannt.
His withdrawal from the party became public yesterday.
Nach dem Eintritt in den Verein bekam sie eine Mitgliedskarte.
After joining the club, she received a membership card.