How to clear a 4 bit shift register with no clear input?
If you don't want to set the parallel inputs to zero, then the only option is to switch the device into shift mode, set serial input to zero and generate four serial clock pulses.

Check the "mode select" table in the datasheet, how to change mode safely, as switching the mode with certain states of parallel and serial clock inputs leads to undetermined operation of the device.

The safest solution is to switch the mode when both clocks are in low (zero) state.

Having said the above, I still consider, that using the parallel inputs, set temporarily to zero by additional logic, may be a simpler solution...