Unlike fame with the higher powers, which is needed to get access to certain teleport pacts, and fame with the civilisations, which is needed for citizenship as well as to take certain rites, raising tribe fame has no global benefits.
Once upon a time there were plans to have tribe fame play a crucial role in guild missions, outposts, and who knows what else? Unfortunately this was never implemented and guild tribe fame was even done away with completely. The benefits of tribe fame today are few and meager.
The easiest way to get your fame up with a tribe is probably to go the tribe's camp and take missions from the welcomer, and to repeat this one per day. If your fame with the tribe is lower than -50, but not lower than -65, you can still take missions from the welcomer, but the camp guards will attack you if you try to talk to him