Of Honorable Lineage
Venerable
い adjective
Someone or something whose 由緒 (lineage) is 正しい (correct) is of honorable lineage, and venerable indeed.
ゆいしょただしい
You already know the readings for 由緒 and 正しい so you just need to put them together to read this word.
彼は由緒正しい家系の出身です。
He is from a family of honorable lineage.
ここは元々は由緒正しい神社なんですよ。
This place was originally a venerable shrine.
由緒正しい生まれの女性に恋をしてしまった。
I have fallen in love with a woman of honorable lineage.