Note: The spelling 'bleeding-edge' is used for meaning 2.
1.
If you are at the ~ of a particular field of activity, you are involved in its most advanced or most exciting developments.
McNally has spent 17 years at the ~ of computing.
N-SING
2.
Bleeding-edge equipment or technology is the most advanced that there is in a particular field.
...an RAF facility with bleeding-edge electronics and communications systems.
ADJ