A cloister is an architectural feature in monasteries, convents, and other religious institutions.  The Cloister is a drink that comes from an unquestionably non-religious institution: the Playboy Bartender's Guide. Published in 1971, the book and the Cloister are my age. In 2011 Jim Meehan, who created the Brown Bomber and the Newark, mentioned the drink in his PDT Cocktail Book.

1.5 ounces gin
.5 ounces yellow Chartreuse
Juice from 1/8 grapefruit
Juice from 1/4 lemon
.25 ounces super simple syrup

Combine in a shaker with ice, shake with the resonant rhythm of a Gregorian chant (which I like), and strain into a chilled glass.  Grapefruit peel garnish optional.

Considering the word cloister, either used as a noun or verb, frequently comes up in connection with monks, it's no surprise the Cloister contains Chartreuse. As we see in cocktails such as the Last Word, gin and green Chartreuse go well together, but for the Cloister you want to go yellow. The Phil Collins also combines gin and yellow Chartreuse, which is a key part of non-gin drinks such as the Diamondback. Along with the super simple syrup, the yellow Chartreuse keeps the Cloister from being overwhelmingly tart.

Have a Cloister, and you may have a, dare I say, religious experience.