The Doctor's mobile emitter was 29th century tech, so they must have a better version of it by the 32nd century. Think Eli, but mobile.
I could see Saru being promoted to Rear Admiral in charge of operations of something. Then he could still go along with Discovery whenever needed.
If you have Discovery as part of a fleet, then Saru could be the Rear Admiral lower half (a.k.a. UK Royal Navy rank is commodore) of the fleet and he could travel on Discovery. That would make Discovery the flag ship of the fleet underway (because Discovery would be traveling with the Flag officer). A flag officer is any officer above the rank of captain.