He was a federal marshal who is informed by Private Investigator Jacob Elway that Hannah McKay is back in Miami, going under the alias 'Maggie Castner' (based on what Debra Morgan had told him earlier).
In pursuit of Hannah, he eventually comes to suspect that Dexter Morgan has resumed his relationship with her and the two are planning to leave Miami together. When he voices his suspicions to Debra, she immediately dismisses them (she is in fact, helping Dexter hide Hannah). However, after Harrison hurts himself while playing on Debra's treadmill, Hannah is forced to expose herself while taking him to the hospital (who at this point, can't get in touch with Dexter). A receptionist there recognizes her and soon informs Clayton that she was at the hospital with her "son". When Clayton sees the name 'Debra Morgan' written on the waiting list, he believes that Debra is harboring Hannah.
After discovering that Dexter Morgan was romantically involved with her and that he wishes to leave the police force at the same time she's rumored to be here, it hits him that Dexter may have re-established relations with her somehow. He voices his suspicions to Debra, but she immediately dismisses them. However, Clayton doesn't buy this ruse after discovering her name written down in a doctor's office after Harrison gets hurt (in reality, this name was written by Hannah, since she was not related to Harrison and needed to use a fake name). Clayton suspects that she is hiding something, so he begins vetting her in hopes that she will lead him to Hannah.