To Stick With, To Stick To, To Go Through
transitive verb, godan verb
This is a combination of the words 貫く meaning "To Go Through" and 通す meaning "To Let Pass." So when you're trying to go through an area and also let someone pass with you, you start to follow them. Not intentionally, but you're both trying to go through at the same time so you decide to stick with them.
This is a combination of two words you already know, so you should already know this too!
He stuck to his beliefs until the end.