I'm 13 and I hack horses all the time. My parents aren't there but my trainer is in the ring usually teaching another lesson and stuff. Its also a barn rule so ask your barn manager or your trainer and the horse owner as well. But totally, unless its not allowed at your barn or the horse owner is uncomfortable with it, go for it!
I would check with the owner of the horse to make sure, if nothing was agreed on in the lease. But unless your barn has rules for that, I would say totally! I do it all the time with my lease, but for some leases there are restrictions.
If nothing was agreed in the lease agreement on that and there’s no such rule at your barn I don’t see why you couldn’t. I, for one, have ridden without parental supervision since I was like 12 whenever I haven’t had a lesson (also on lease/whatever it’s called ponies) and there’s never been any issue, of course it’s always safer to have someone with you :)