To Stick To
To Carry Through
transitive verb, godan verb
This is a combination of the words 貫く (to go through) and 通す (to let pass). Literally, it can describe piercing fully through an object. However, 貫き通す is usually used figuratively to mean to stick to something to the very end. Just like piercing an object from one side to the other, 貫き通す implies you push forward no matter what, sticking to your beliefs or determinations all the way.
This is a combination of two words you already know, so you should already know this too!
彼は最後まで自分の信念を貫き通しました。
He stuck to his beliefs until the end.
自分のスタイルを貫き通すのは、思ってるほど簡単じゃないよ。
Sticking to your own style is not as easy as you think.