Drill and dowel the old footer to the new as Dennis said but my professional opinion is that you shouldnt cut the siding away. If there is plywood or osb behind the siding or better yet a stud ,screw the block tie in the cove part of the siding,snug but not overly tight enough to buckle the vinyl. Not that you should do it but ;I had a job putting a two story addition on the gable end(brick all the way up) and had to remove all the old brick. There were, no exaggeration, SIX brick ties in the whole thing
There had been no movement at all in some sixty years the house had been there. If you have no movement in the footer youll have no movement in the chimney. Fill the bottom of that hole with #3500 lb concrete to the top of the existing footer and rock on. And good for you on the masonry chimney.