Yes, the tribal king will invite the clan chieftain and will ask for his support in politics, raids and wars. The king and the other chiefs might not know the new character and will try to figure out where he stands and what his motivations are. Always remember that a tribe does not mean they are all friends. Sometimes your worst enemy is in the same tribe as you.
If tribes are not that important in your Glorantha, there is still plenty of room to get to the next level. No clan is a one-person show. There is always the clan ring. The player characters might even be on the inner clan ring, giving direct advice to the chieftain. That way the players see that their decisions matter and that they have a responsibility for others.
If you have used the clan questionnaire the clan already has some ancient allies and enemies. It's a good way for you to involve the players in large scale conflicts.
You can also point out to your players that it is impossible to make friends with everybody. If they are already allied with the Lunars they might find it difficult to make friends at Geo's Inns or in Whitewall. On the other hand King Kangharl of the Colymar tribe or Darsten Black Oak in Runegate might be more favourable towards them. However, if your Issarite is the only Lunar sympathiser, her own clan might regard her a traitor...
Good luck and have fun.
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