There was no High King in 1066; there hadn't been one since 1022 and wouldn't be one until 1072, and even then he was a "High King with Opposition"...
As for the Norse kingdoms: the Kingdom of Dublin was occupied by Leinster in 1052 and would only re-emerge periodically from native occupation for much of the next century (Dublin was independent from c. 1070 - 1074, c. 1091 - 1094, 1118 - 1124, 1127 - 1141 and finally from 1142 - 1171, after which it was occupied by the English). The Kingdom of Limerick was permanently annexed by Munster in 978, and the Kingdom of Waterford was annexed by Leinster in 1037 and would only re-emerge in the years just before the English occupation in 1170/1. So in 1066, there were no independent Norse states on the island...