The transition altitude is an altitude (based on QNH) but the transition level is a Flight Level (based on 1013.25 mb).
Yes you can fly at the Transition Level whilst complying with the Quadrantal Rule. (Equally you can flt at the Transition Altitude but this would not be in accordance with the Quadrantal Rule because the latter is based on 1013.25 and magnetic track).
An aircraft is flying on a magnetic track of 075 degrees. The QNH is 1010. What is the lowest available flight level to fly in accordance with the quadrantsl rule?
Assuming the Transition Altitude in this case is 3,000 ft amsl then the Transition Level would be FL 35. Since we are in the first quadrant an ODD flight level is appropriate so in this case Flight Level 50 would be appropriate.
Hope this helps!