These brief summations are from the post-Revival Trials to late 3050s:
Blood Spirits - After their failed attempt to join the invasion, they once again isolated themselves until the Burrock Absorption. Their interference cost them significant military strength and once again they isolated themselves from the other Clans after this perceived betrayal so they could focus on rebuilding.
Burrock - Little canon information is available although it is known that they took advantage of the Fire Mandrills' weakened state to retake territory previously lost to the Mandrills before the Star Adders revealed their illicit dealings with the Dark (or bandit) caste which ultimately led to their absorption by the Star Adders.
Cloud Cobras - Little is stated of what they were up to during the invasion years. It can be speculated that they largely kept to themselves, defending themselves when necessary and launching occasional attacks against their neighbors (as dictated by the Way?).
Coyote - Due to the predations by other Clans, Clan Coyote's touman was critically understrength by the mid-31st century. Much of the 3050s was spent reorganizing the touman. Several clusters as well as four entire Galaxies were disbanded and their remaining warriors reassigned to shore up the remaining units causing considerable internal tensions.
Diamond Shark - Yeah, yeah, they were briefly activated but for most of this time period they were effectively a Homeworld Clan. After Clans Steel Viper and Nova Cat were activated by ilKhan Ulric Kerensky, they were bitterly disappointed to be given the role of Reserve Clan. While this did allow them to participate in the Battle of Tukayyid, poor leadership decisions led to almost all their forces being destroyed and were forced out of the Inner Sphere as a result. After the battle, they focused their efforts on rebuilding their forces and defending their holding against Clans seeking to take advantage of their weakness. As a byproduct, the Clan started shifting back to their traditional Warden views. This shift increased as many Crusaders forwarded challenges to the Invading Clans in order to rejoin the invasion. The slots were usually quietly filled with Wardens.
Fire Mandrill - In the wake of heavy losses before and in the Harvest Trials, the Hellions' Fury campaign and Burrock predations, Clan Fire Mandrills' Kindraas largely focused on rebuilding and trying to retain as much territory as possible.
Goliath Scorpions - They focused on increasing their strength by launching numerous strikes to probe neighboring Clans and trying to significantly modernize their aerospace forces.
Hell's Horses - They largely kept themselves out of most of the fighting that engulfed the Clan Homeworlds and focused on rebuilding.
Ice Hellion - To avoid internal fighting, their Clan turned his warrior caste's anger at being knocked out of the Harvest Trials again the other homeworld Clans allowing them to vent their anger while gaining numerous lands and resources but costing them invaluable warriors including their senior Khan. After the failure of the Invading Clans at Tukayyid, the Hellion Khans tried to rally the remaining Homeworld Clans to pressure the Invading Clans into allowing more Clans to join the invasion. These efforts were ultimately frustrated with the Harvest Trials.
Snow Ravens - In exchange for invaluable trade concessions (including access to Inner Sphere resources), the Ravens contracted out a significant portion of their WarShip fleet to the Jade Falcons until a dispute led to a breakdown in relations. Outside of that they remained largely aloof from the infighting among the Homeworld Clans and chose not to join the Hellion's coalition to force the invading Clans to allow more Clans to join the invasion. Their attempt to humble the Jade Falcons during the Harvest Trials backfired costing them more than two Clusters as well as their saKhan before they could extricate themselves from the mess.
Star Adders - Like several of their fellow Clans, they struck out against their neighbors in order to create a new dominant Clan among the Homeworld Clans. They stepped up their efforts against the Diamond Sharks after hearing about their losses at Tukayyid. They would reveal Clan Burrock's illicit dealing with the Dark Caste and would ultimately be rewarded with the right to absorb them. After the absorption, they would focus on integrating their new members and rebuilding from the losses (largely the result of the Blood Spirits' interference in the Trial) in preparation to taking the fight against their new enemies.
