Nがゆえ=Nゆえ=because of N (N is the reason)

重要であるがゆえ、連絡先のみのセクションが分け与えられているのである。
Because it's important it is that the section that has only the contact information has been distributed(assigned on the page)


*XゆえのY=X-based Y; Y by reason of X　(E.g. 女性ゆえの差別 → "womanhood-based discrimination/discrimination by reason of womanhood")


天才ゆえの余裕
leeway someone has because he's a genius


訓練の成果と、未来を知ってるがゆえの余裕もあって、俺は...
I, who has leeway(freedom to act(as in having more options available)) by reason of practice and knowing the future,...
=
I had practiced and had the benefit of knowing the future, so I ...