〜を経て
through, after going through, via
Noun + を経て
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を経て means passing through a stage, process, place or length of time on the way to a result: 厳しい審査を経て、代表に選ばれた, "after a rigorous selection process, she was chosen as the representative".
It works with processes (審査, 交渉, 議論), with time (十年の歳月), and with places on a route (ソウルを経て東京へ). The second half is where you ended up.
Compare を通じて (N2), "through (a channel, or throughout a period)". を経て stresses completing each stage in order before moving on.
経る (へる) means "to pass through", and 経由 (via) uses the same kanji.
Examples
厳しい審査を経て、代表に選ばれた。
After a rigorous selection process, she was chosen as the representative.
長い交渉を経て、ようやく合意に至った。
After long negotiations, they finally reached an agreement.
飛行機はソウルを経て、東京に到着した。
The plane arrived in Tokyo via Seoul.
十年の歳月を経て、建物が完成した。
After ten years, the building was completed.
様々な困難を経て、今の会社がある。
The company is what it is today after going through all kinds of hardships.