Peers has two meanings:
1) verb: to look or gaze. For example: He peers at the puppy through the window. (that is, he looks at the puppy through the window)
2) noun: Individuals who are comparable on some given metric. For example: My peers and I met to discuss issues which impacted our lives.
Peer's refers to something belonging to a single peer (definition two above).
For example: I thought that my peer's sweater looked very nice on him.
Peers' refers to something belonging to a group of peers (definition two above). For example: As a group, my peers' achievements are very impressive!
So for your sentence on taking advice, I would assume that you would want
to use "peer's", because it refers to the advice which comes from a single peer.