A TRACON Controller reported when they relieved a controller they did not realize the previous controller had not climbed an aircraft to the altitude in the new arrival and departure procedures resulting in a conflict with another aircraft at the same altitude.

Narrative

I was told to get someone out of position who was going home in next 15 minutes. However Controller working right next to this Controller said he was skipped for a break and had almost been in position for 2 hours. The break board (Software program at ATC work areas where Controllers sign in and out of the area and duty) was incorrect! This started a conversation with the Supervisor of a back and forth conversation. Meanwhile I plugged into position get this person out who was almost skipped. The briefing was only that I had 2 planes. Problem was one of them was stopped at 5000 feet and was never climbed up to the required altitude of 6;000 feet to get above the final traffic.Even though I own this airspace it's a built in trap because I deliver planes at 5;000 feet from the west. The last plane was switched that would have been a conflict. Normally with our old procedures it would have been a no brainer. I asked the Controller next to me to verify do I have to climb this plane they handed off to me or is 5;000 feet ok. We have had so much changes with new airspace design; a lot of people are having close calls because there are so many traps and people are unsure of what altitudes are correct. Once I realized my error I turned and climbed the plane to get away from conflicting traffic. Biggest problem is people clear aircraft for ILS at 5;000 feet and pilots don't descend until they intercept the glideslope which is probably about 14 miles west of field. You would be perfectly legal to clear the aircraft at 2000 or 3000 feet and when clear to cross ZZZZZ at 5;000 feet for ILS XXL the trap is set. We had so many changes at once with Aircraft X and descend via and climb via which has caused more bad than good for some Radar positions. Heavy workload lots of conflicts and confusion on right thing to do for the AR-P scope.