When I did a Harvest Tournament in my campaign, I had a few competitions, such as Axe Throwing, Archery, Caber Toss, and Tilting.
Each competing character first got three rounds of Practice. They rolled an appropriate Skill or Ability Check, and then were rewarded dice:
Practice Results
20+ ... d12
15 - 19 ... d10
10 - 14 ... d8
5 - 10 ... d6
1 - 4 ... d4
There were three rounds to each competition. The competing characters again made a Skill or Ability Check, then got to add in any Practice Dice they wanted to. Whoever had the highest results for that round won.
Round Order
1. Roll Skill or Ability Check
2. Add Practice Dice (optional)
3. Tally points!
I designed a handful of NPC's who were competing. I gave them their own Practice Dice to differentiate them.
So for example, competing in the Archery Tournament might be:
Clumsy Clarence (+1 Archery)
Practice Dice: 1d4 1d4 1d6
Pretty Good Pauline (+3 Archery)
Practice Dice: 1d6 1d8 1d10
Bullseye Betty (+5 Archery)
Practice Dice: 1d10 1d10 1d10
I let all the NPC's go before the characters so that they could decide how many practice dice to add in.
Oh, I also had side bets going on, so players could bet on who they thought would win!
For a fishing tournament I would organize it this way:
Before the Tournament, characters have a chance to prepare. They can do so through a few ways: purchasing or crafting equipment, scouting out fishing spots, researching local fish, etc. I'd allow them to make Ability or Skill Checks to earn one Favor Die each, which gets added to a group pool of Favor Dice.
So let's say the Druid communes with nature to learn about what fish are in the lake and makes a Wisdom (Nature) check, rolling a total of 15 and earning a d10. The Fighter goes to the fishing supply shop and scouts out really good poles, making an Intelligence (Investigation) check and rolling an 4, earning the group a d4. The Cleric prays to their god for favor, makes a Charisma (Religion) check and rolls a total of 20, getting the group a d12. The Rogue tries to sabotage the fishing boats of the competition, rolls a Dexterity (Thieves' Tools) check and gets a 10, earning the group a d6.
The group's Dice Pool is d4, d6, d10, d12
On the day of the tournament, have everyone describe what they are doing in order to catch fish. Maybe they are trying to use their Strength to fling out really far. Maybe they are being really smart about where to cast. Maybe they are just reaching in with their big hands and trying to grab a fish.
Roll for all the competing NPC's, then allow each character to roll an appropriate Skill or Ability Check.
Have each NPC set up with one Favor Die that they roll in, describing each of their unique fishing poles, boats, skills, or magic. Then invite the characters to do the same.
Most likely they will confer and decide whoever rolled the highest ability check will use all the dice! Say "Oh man, I didn't think about that! Great idea!"
There you go! There's a chance for an NPC to win, but a greater chance for one character to win. Everyone gets some fun scenes of preparing for the tournament and competing.