There is no need to change the locks on your old home when you move out of it – the new owner should do this themselves. You should definitely change the locks on your new home when you move in – and this should be a priority!
You have no idea how many keys exist for the old locks, or to whom those keys belong. It is also a common practice for estate agents to put their copy of a key on a keyring marked with the address of the property.
It’s a small cost, but a huge benefit. If you moved into a new property and you were burgled by someone who used a key, your insurance company would not pay out.