Traditionally regarded as one of the most powerful Orcadian earls, Sigurðr appears to have extended his authority into the Isles in the late tenth century.

It is possible that Gilli is identical to Gilla Ciaráin mac Glún Iairn, an Uí Ímair dynast who was slain at the Battle of Clontarf in 1014.

[11] Contemporary Orcadian expansion may be perceptible in the evidence of the land-assessment system of ouncelands in the Hebrides and along the western coast of Scotland.

[12] If Sigurðr's authority indeed stretched over the Isles in the last decades of the tenth century, such an intrusion could account for the numbers of silver hoards dating to this time.

[15] Although it is not impossible that the Danair (perhaps merely meaning "pirates") refer to Sigurðr's forces,[16] it is more likely that they are instead identical to the Vikings who are otherwise attested attacking England in the 990s.

[19] This could indicate that either the kin of the recently deceased Amlaíb Cuarán, King of Northumbria and Dublin,[20] or perhaps an Orcadian-aligned Islesman like Gilli himself, may have fallen target to an alliance between the Danair and Guðrøðr.

[22][note 4] The extent of Guðrøðr's authority in the Hebrides is unknown due to his apparent coexistence with Gilli, and to the uncertainty of Orcadian encroachment.

[29] Although it is conceivable that either Gilli or Sigurðr capitalised on Guðrøðr's death, and extended their overlordship as far south as Mann, possible after-effects such as these are uncorroborated.

[41] Certainly, Eyrbyggja saga states that Sigurðr left menn ("agents") in the Hebrides to collect tax from Mann,[42] whilst Orkneyinga saga reveals that, at a later period in time, Sigurðr's son and successor, Þórfinnr Sigurðarson, Earl of Orkney, tasked a member of his own wife's family, Kálfr Árnason, to impose Orcadian authority in the Isles.

In one instance, a Caithnessman is said to have witnessed valkyrie-like apparitions singing songs for the slain, whilst a similar event is said to have occurred in the Faroe Islands.

Regarding Gilli, the saga asserts that he dreamt of a song that foretold the outcome of the battle and the fall of Brian and Sigurðr.

[54][note 7] If the account of Gilli in the aftermath of Clontarf has been constructed for dramatic effect, the passage may not be evidence of his floruit beyond this point in history.

[57] The Annals of Ulster, which records the latter's fall, styles him rígdamna Gall ("heir-designate of the Foreigners"), revealing that Gilla Ciaráin was indeed a prominent man.

If Gilla Ciaráin was a son of this king, his apparent tender age at the time of his father's death could account for Sitriuc's accession to the kingship.

In 980, Máel Sechnaill mac Domnaill, High King of Ireland utterly defeated Amlaíb Cuarán's forces at the Battle of Tara.