You can refer to a man who used to be a pupil at a particular school or university as an old boy.
[British]
...Eton College, with all its traditions and long list of famous old boys.
...Cardiff High School Old Boys rugby team.
Synonyms: alumnus or alumna, former pupil More Synonyms of old boy
2. countable noun
If you refer to an old or middle-aged man as an old boy, you are referring to him in a disrespectful way.
[British, informal, old-fashioned, disapproval]
Outside, two old boys lingered on the street corner discussing cattle.
old boy in British English
noun
1. (sometimes capitals) British
a male ex-pupil of a school
2. informal, mainly British
a.
a familiar name used to refer to a man
b.
an old man
old boy in American English
1. [sometimesO- B-] Chiefly British, Informal
an alumnus, esp. of a boys' preparatory school
2.
a man belonging to a social, professional, etc. group regarded as prestigious or influential, whose members provide one another with assistance or preferential treatment