Your trigger has one major flow.

When INSERT operation is performed the TRIGGER is fired for an operation, not for every inserted record.

The way your trigger is written it will only process your logic for one of the inserted records.

You should never read from INSERTED or DELETED into variables in triggers.

Here is example of how it should be done properly:

ALTER TRIGGER TR_Update_Interaction

ON dbo.cust_hist

AFTER INSERT AS

BEGIN

SET NOCOUNT ON;

UPDATE cust_hist

SET notes = v.consignment

FROM cust_hist ch

JOIN inserted i

ON i.tkey = ch.tkey

JOIN VLoadnoteCarr v

ON v.load_note = i.primary_ref

END

Now, if it still doesn't update as expected, you need to analyse JOINs. Are they using relevant key columns?