Yes, once you beat the E4 and champ, you have completed your Island Challenge. But, afterwards, you have the post-game to complete.
Here are some suggestions on completing the Post-Game:
1.) Completing the Pokedex.
2.) Going to the Hano Grand Resort and chucking Pyukumuku (Once you chuck all 6, talk to the man who gave you this assignment and he will award you with $20,000 Pokédollars).
3.) Doing the Ultra Beast side-quest and collecting all of the Ultra Beasts (once you complete this, you can catch Necrozma at Ten Carat Hill).
4.) Battling and capturing the Tapus.
5.) Collecting all 100 Zygarde cells/cores to turn Zygarde %10/%50 Forme into Complete form when its HP drops below 1/2.
6.) Batting GameFreak director Morimoto in HeaHea City (its the 3rd floor of the building next to the Dimensional Research Lab building).
7.) Checking the Loto-ID on Melemele Island (its the building next to the apparel shop).
8.) Taking photographs using the Rotom-Dex (You get an award for acquiring 1.5 million thumps-up).
9.) Rebattling the Trail Captains.