It's called a messenger..... it your halyard is all rope you can use the old one as the messenger... connect the two lines together, end to end, with a paper clip, or sew it together, then wrap some tape around it. You're now ready to reave the new halyard.
If you're replacing a wire/rope halyard, the sheave up top may accommodate the rope part .... in that case, clip off the shackle and tie a length of THIN line to the wire with a rolling hitch.... then wrap with tape..... now you can pull the messenger through, attach the new wire in the same way and use the messenger to pull the new halyard back into place.