To clarify further, it really comes down to points and you need to complete a certain number of points to move on to the next tier quest line. It breaks down like this:
- Tier 1 Line: 7 points to complete, 1 point per T1 quest
- Tier 2 Line: 14 points to complete, 2 points per T2 quest
- Tier 3 Line: 21 points to complete, 3 points per T3 quest
- Tier 4 Line: 28 points to complete, 4 points per T4 quest
- Tier 5 Line: 35 points to complete, 5 points per T5 quest
- Tier 6 Line: 42 points to complete, 6 points per T6 quest
The math works out so that you need to complete
at minimum 7 quests to complete a tier line (as long as those quests are of the same tier level as the current quest line you are on). Since all you need is the total number of points, you can technically complete lower-tier quests and those points will go toward your current line. For example, if you complete tier 1 line, you can do 14 additional tier 1 quests and you will complete tier 2 line; or do 2 x t5s, 4 x t4s, and 3 x t3s (which would add up to 35 points) to complete tier 5 line.
Why would anyone do that? It really depends on what you are looking for. Quest rewards change based on tier. If you are looking to get forged steel quickly in the early game, completing tier 3 quests is sometimes the better option since 3s are quicker and easier to do than 4s or 5s and there's almost a guaranteed reward option of 25 forged steel. Fetch-only quests also end at tier 3, so if you are looking to complete quests more quickly to complete a higher tier line.
It's been like this as far as I can remember (but I've only played since A19). And as was mentioned before, each time you complete a quest line, you'll get a special job to find a trader. But you do not have to find said trader in order to move on to the next tier. You just have to wait to the next day (or log off then back on) to get offered the next tier of quests.