Throughout The Alola Region are given characters looking to see the Pokedex Entry Information for specific Pokemon. In return for showing them after catching said Pokemon, they will give you a substantial amount of Money (usually). There are no Time restrictions for the Quests, and it isn't necessary to have the Pokemon in your Party either.
Pokedex Quests
Melemele Island - Hau'oli City Pokemon Center - Drifloon - $10,000 Reward
Melemele Island - Route 2 Pokemon Center - Cutiefly - $3,000 Reward
Melemele Island - Route 3 - Rockruff - $3,000 Reward
Akala Island - Heahea City Apparel Shop - Pyukumuku - $10,000 Reward
Akala Island - Konikoni City Pokemon Center - Oranguru/Passimian - $5,000 Reward
Akala Island - Route 5 Pokemon Center - Feebas - $3,000 Reward
Akala Island - Route 8 Aether Trailer - Stufful - $5,000 Reward
Ula'ula Island - Malie City Apparel Shop - Togedemaru - $10,000 Reward
Ula'ula Island - Maile City Library - Alolan Persian - Love Ball
Ula'ula Island - Route 16 Pokemon Center - Mimikyu - $20,000 Reward