Team perks are a great idea that add to being on a team with high skilling levels. Here are some suggestions I have to improve on what exists, and add to what yet doesn't.

Woodcut, Mining, Fishing

Current Perk: Chance of noted logs, fish or ores at level 80.

Suggested change:
1. Chance of noted logs, fish or ores scales at every 10 levels starting at 60.

Reasoning: While 80 is a good requirement for a large team, it may be difficult for a team of just a few members to accomplish without excessive grinding, especially since it seems that team experience is gained on a scale that matches original xp, without any benefits from subscription bonuses.
Now, this doesn't nerf the extant perk -- the bonus would scale every ten levels, matching the current chances at 80.

2. Chance to double gather, scaling every 10 levels starting at 70.

Reasoning: The cost of materials is, at current, too damn high. This will add materials to the economy in slightly greater numbers, lowering their cost slightly due to higher supply. It will also make the gathering process slightly faster, increasing xp rates by a small amount. This will be especially useful for gathering high-respawn time resources like coal or magic logs.
One must tread lightly in its implementation as to not increase the supply by too much!

Thieving

Current Perk: None

Suggested Change: Chance of double steals scaling at every 10 levels starting at 60; better pickpocket chances scaling every 10 levels starting at 80.

Reasoning: This would be a cool way to add a set of perks. It would make early game team members less frustrated with pickpocketing success rates, as well as boost their potential gains from thieving. For late game team members, it would boost their experience rates.

Agility

Current Perk: None

Suggested Change: Hidden +1 bonus to agility level per 10 levels of team agility starting at level 30. This would mean that you could use certain shortcuts earlier. So if your team has:
30: +1
40: +2
50: +3
...
99: +8

Reasoning: Agility is a long grind for everyone involved. If an entire team works on it together, they'll all reap the benefits of the shared experience they've gained.

New Perks

Some of the skills in game don't have perks, but would benefit from them greatly. Here are a few suggestions.

Cooking

Suggested Perk: Chance to double cook scaling every 10 levels starting at 60.

Reasoning: This would speed up the process of cooking, but wouldn't get out of control since it's not 'multicook'. This could help when preparing for team outings: Preparing by fishing together, then cooking together.

Smithing

Suggested Perk:
1. Higher chance of refining ore scaling every 10 levels starting at level 50.
Reasoning: Iron really should scale as you get better at smithing anyway; this is a great way to introduce it. Again, this will make smithing less frustrating for early game players, and more profitable for late game players.
2. Chance to double smelt scaling every 10 levels starting at level 70.
Reasoning: This will increase experience and production rates, dragging down the cost of materials slightly due to greater expedience in finishing inventories. One must tread lightly in implementing this as to not increase the supply too much!

Herblaw

Suggested Perk: Chance to ignore secondary ingredient scaling every 10 levels starting at level 60.

Reasoning: Finding secondary ingredients can be time consuming and expensive. Ignoring secondary ingredients will help to make herblaw a little bit more livable, and bring the overall cost of creating a potion down while keeping profits intact. This would occur when you use the secondary ingredient on the unfinished potion, since a few potions use the same primary herb.

Conclusion

These are just a few suggestions to improve an already amazing system. As of now, the perk system feels incomplete: this is not a dig on the development team, it is very obvious that this is still under development. The improvements I've outlined will make being on a skilling team more valuable, bring the incredibly high cost of materials down, and add great bonuses to certain difficult to train skills.

Thank you for reading!