pre-noun adjectival
Literary pre-noun adjectival meaning 'past' or 'former', used to refer to a time, state, or thing that once existed. Often appears in nostalgic or reflective contexts.
在りし日の思い出がよみがえる。
Memories of past days come back to me.
在りし姿を写真で見る。
I see his/her former appearance in a photograph.
pre-noun adjectival
when one was alive; during one's lifetime
Specifically refers to the time when someone was alive, often used in eulogistic or memorial contexts. The person is typically deceased.
在りし日の父を思い出す。
I remember my father as he was when he was alive.
在りし日の彼女の笑顔が忘れられない。
I can't forget her smile from when she was alive.
昔 is a common noun meaning 'old times' or 'long ago', while 在りし is a literary pre-noun adjectival that directly modifies a noun to mean 'past' or 'former'.
かつて is an adverb meaning 'once' or 'formerly', used with verbs, whereas 在りし is a pre-noun adjectival that attaches to nouns.
Derived from the classical Japanese verb あり (to be, to exist) in its 連体形 (attributive form) ありし, which functioned as a pre-noun adjectival. The kanji 在 is used for existence in a place or state, while 有 is used for possession or occurrence; both are acceptable here.