Hey @Helen S
Not sure of your budget but there are many good basses in the £200-300 range - so much so that he won't NEED to upgrade but will eventually WANT to.
There are numerous threads here about budget basses - held in esteem include Sire, Musicman Sterling, Yamaha, Spector and Squier. I've owned one or more of each brand and not been disappointed, selling only because of that eternal search for the "perfect tone" - which probably doesn't exist anywhere other than between my ears.
Unfortunately, if your son joins this forum you won't be able to block the Marketplace options so he will inevitably contract GAS (Gear Acquisition Syndrome) like the rest of us older kids.