If the old External Hard Disk is 5 years or older, it would be extremely wise to replace it. All HD's wear out, some last 2-3 years some last 10 years so you never know when they will fail, and they often fail with no advance notice! Replacing them about every 5 years is not a bad idea, for a backup drive like Time Machine it is extremely smart as you always want a working backup.
Also when buying a drive it is wise to buy a high quality External Hard Disk such as a OWC Mercury Elite Pro. Buying Walmart quality drives such as WD, Toshiba, Seagate etc is not smart as their enclosures are cheap and do not provide adequate cooling and heat is generally a common killer of electronics.