P80 Controller described a loss of separation event when departure traffic unexpectedly climbed into occupied airspace; the error traced to an incorrect altitude assignment issued by Clearance Delivery.

Narrative

I was working Hood Sector which in an arrival and departure sector. A DH8D; departed PDX southwest bound climbing to 3;000. After RADAR identifying the aircraft; I instructed them to climb to 8;000 and turn left direct to TIMEE intersection. While the DH8D was in the turn; I noticed a departure tag up south of PDX on a Newberg tag; which is an adjacent sector. I called traffic the traffic to the DH8D; which was a B350. The DH8D did not have the aircraft in sight; which was not a worry to me as the B350 should initially be climbing to 3;000 and the highest that Newberg can climb them is 4;000. I kept watching the B350 and noticed them climbing fast through 3;000 and again issued the traffic to the DH8D; but they still did not have the aircraft in sight. When I looked back I saw the B350 at 4;200; so I immediately displayed the DH8D to the Newberg Controller and questioned them on what the B350 was doing. They immediately issued a turn to the B350; who informed the Controller they were climbing to 9;000. I later found out that the aircraft had never checked in on frequency and that Clearance Delivery in the Tower incorrectly gave the pilot 9;000 as their assigned initial altitude. The DH8D and the B350 eventually got each other in sight when they were at the same altitude and a little less than a half mile apart horizontally. Recommendation; Clearance Delivery; who issued the incorrect altitude; was newly certified on that position in the Tower. I'm not sure of this Controller's background and if this is their first position or not; but maybe more supervision needs to be done on newly certified controllers. It's possible that the Clearance Delivery Controller's training time was inadequate and that more time training would be helpful. It also was found that Local Control waited longer than normal to switch the B350 to departure and was confused on what frequency to give the aircraft. Timely switching to the Departure Controller; where they would have hopefully heard the incorrect altitude the aircraft was climbing to; would have prevented the incident.