If you have a soft eye on the bitter end, you can tie on a reeving line the existing line out to pull it out and pull in the new line. I use a bowline to tie off the lines.
Otherwise lIke Dave said, you can stitch the butt ends together and hope for the best. You can wrap the spice in rigging tape for extra insurance.
When I change out any of my running rigging, I always have it made up with a soft eye (reeving eye) on one end and a structural eye on the other end for a shackle.
This also comes in handy when we remove our halyards and topping lift for the winter. Even tho we shrink wrap our boat, it doesn’t protect exposed halyards up the mast from slapping and chafing, no mater how tight they are, during a brutal New England winter.