hi ico,
Assuming the Up counter has parallel outputs of the 4/8 bits and assuming the Shift register has a parallel load option.
If its made up of 'D' type FF's then it has the equivalent, the 'D' inputs.
Just connect the outputs from the Counter to the respective input 'D' bits of the Shift register.
Generate a clock/para load pulse into the Shift reg to load the Counter into the Shift reg.
Is this what you mean ico ?
Do you have a drawing of your circuit?
EricG