After you beat Red, is that the end of the storyline? Apart from getting the numbers of the leaders and stronger elite four is there anything else?
No more Team Rocket? No more Red-Haired guy?
Iso answers

red hair guy appears at poke league on weekends or something for a battle, i think you can rechallenge the gym leaders? theyre stronger

keep rebattling people you got pokegear numbers for, every time you battle them the pkmn get stronger.