Unlike most stringed instruments where the sound must go through a bridge or nut and can always be picked up from one (or very few common) locations, the principal source of sound for a clarinet or other keyed instrument comes from a different place for each note. The common solution is to use a directional mic located where the 'nettist can "blow at it." If the mic is sufficiently directional, her monitor noise can be directed at her head and away from the mic to eliminate the feedback.

If your clarinetist is geeting feedback, she's likely getting enough pickup, or too much. What you need is more likely a preamp, preferably with some volume control, between her pickups and your PA.

As a personal note, I would not voluntarily remain in any environment where I couldn't hear my own clarinet. Played at normal volume two or three clarinets in the same room can cause damage to one's headbone. It's a very "strong" instrument. If she's having trouble getting normal loudness, perhaps a step - or half-step - up in reed stiffness, and a little practice with the harder blow might help more than changing pickups.

John