You cannot clear the shift register by applying a control signal. You must serially write zeros to it.

The 4094 contains three independent sections: The shift register with DATA and CLOCK input, an output latch with STROBE input and an output buffer with OUTPUT ENBALE input. You shift data into the shift register, you transmit it to the output latch and emit it by activating the output buffer. The output buffer provides tri-state outputs. So, you can turn-off the output buffer, as if it was not existent.

But there's no way to simultaneously clear all the shift register cells.

Kai