Howdy Jim. There shouldn't be any problem with just installing new drywall over the old. The only reason I would do away with the old, would be if it had deteriorated or had succumbed to water damage.

good luck.

Dave L

You might still consider removing the old drywall if the additional thickness screws up your electricals, moldings, door and window openings or any builtins you might have. I have had to remove and rehang some tight spots where even 1/4 drywall would have been too thick. If not, you can use construction adhesive in addition to screws to attach new drywall over sound old drywall. This cuts down on the number of screws you need to use and tape.