I will preface my answer by saying that things like this are trivial with EOP, but that requires knowledge of Lua scripting and I won't discuss it here as it's not the correct forum for it. I will limit the rest of my answer to conventional (sans EOP) scripting.
The difficulty in realizing your idea is that we're limited to a very small set of valid conditions for building levels and effects in export_descr_buildings.txt (EDB). All EDB conditions that I'm aware of are listed below:
Code:
building_present
building_present_min_level
event_counter
factions
hidden_resource
marian_reforms
port
region_religion
resource
As you can see, none of these make reference to the settlement governor or his traits, ancillaries, attributes, or etc. We could use campaign_script.txt to test if any governor with a particular trait is present in a particular settlement and then set an event counter referencing that settlement to 1, but if we test the value of that event counter in EDB using the event_counter condition, then we've essentially limited the building to only be available in that one particular settlement.
If you really want the building to be buildable normally, there is a workaround I can envision that involves, thousands of monitors in campaign_script.txt (CS), hurting AI turn times, and dozens of building chains just for one governor character. It would require overhauling your hidden resources to set up an exponential system for uniquely identifying all regions on the map, similar to what is described in this thread. You would quickly run out of building chains (hard coded 128 limit) if you were to expand such a script for multiple governors.
Alternatively, you could abandon the idea of normally buildable buildings and use guilds instead. The code in export_descr_guilds.txt for such a guild might look like this:
Code:
Guild HondaClanGuild
building honda_clan_building ;this building must still be set up in EDB, no conditions are needed except the faction or culture type
levels 50 100 300
;[...]
Trigger HondaClanTrigger
WhenToTest SettlementTurnStart
Condition GovernorAttribute Magic == 1 ;perhaps 1 means Honda clan governor, 2 means Ii clan governor, etc.)
Guild HondaClanGuild o 5 ;add +5 guild standing points to this settlement only per turn that this governor is in the settlement, after 10 turns, the guild will be offered
Guild NaomasaClanGuild o -1 ;just for fun and to show what's possible, we can also subtract points from the other clan guilds making it harder for this region to ever be settled by them
The Magic attribute is used by the witch agent in the vanilla game and usually not used for generals/governors in most mods which is why I prefer it for this type of thing. The special trait you set up might look something like this in export_descr_character_traits.txt:
Code:
Trait HondaClanTrait
Characters family
Level HondaClanTrait_A
Description HondaClanTrait_A_desc
EffectsDescription HondaClanTrait_A_effects_desc
Threshold 1
Effect Magic 1
As you can see, the virtue of using guilds instead of normal buildings is that their trigger conditions are much more numerous than the EDB conditions. Additionally, guilds are limited to one per settlement which I think is thematic for the clan buildings you're describing. The second tier of the guild is limited to one per faction and the third tier is limited to one on the entire map which you could also use for thematic effect, for example by making the second tier be the faction leader's residence. The AI might even avail themselves of these guilds (I don't remember if the AI ever builds guilds in the vanilla game).
The basic concept of this guild system is extremely extensible. For example, you could tier the traits so that governors with greater loyalty to the Honda clan, represented by different Magic attribute values, add guild points to settlements faster and subtract points of the other clans' guilds, allowing them to more quickly 'settle' conquered regions. You could go really crazy and convert religions into clans and add a religious conversion effect to the guild buildings in EDB.