free edge
Basically, the two words mean nearly the same thing. The word adhere is a bit more formal than the word follow, so chose based on your audience. In the workplace or in an academic assignment, adhere...
"bind", "bond", "cleave", "cling", "cohere", "hold fast", "stand by", "stick", "stick by" and "stick to"
stick
From the same root, abhere might work (although it is not an official word).