A Center Controller reported an aircraft did not comply with their clearance to climb and flew below the Minimum IFR Altitude.

Narrative

Aircraft X called on frequency to pick up their IFR clearance 31 miles SW ZZZ; which they departed from. They were in an MIA of 9000 [ft] and the aircraft was at 8600. I stated; 'Reaching 9000; you're cleared to ZZZ1 airport via ZZZZZ then as filed. Climb and maintain 14000. They repeated the clearance back the same. Another few minutes go by and I realized they were staying between 8400 and 8700. Never reached 9000 yet. So I called out to them and said to maintain their own terrain and obstruction avoidance. I told them what my MIA was; 9000; and that their clearance was not valid till they reached 9000. They said ok and reported that they reached 9000 just before an MIA of 10000 They hit the MIA 10000 at 9300. I did not give them a safety alert when I should have and shipped them to another frequency. I noticed they still weren't climbing and told the Supervisor what was going on and she immediately told the Area X Supervisor. That Supervisor went and spoke with the current Controller working the aircraft and advised them that they were cleared out of 9000. The aircraft was 2 minutes away from a 12000 MIA and only in-between 10000 and 11000. They went VFR just before the 12000 MIA. I need to be more aware of the VFR to IFR pickups and make sure the aircraft climbs when I give them a clearance. I also need to give a safety alert next time.