Sir Richard Gozney will be paid around £100,000 a year as the Queen's latest representative on the island and live in Government House.
A Celtic League spokesman said using public money to fund the position "was outrageous at a time of austerity".
A government spokesman said the full cost of the role is £400,000 a year including all associated salaries.
Mr Gozney, a former governor of Bermuda, became the Isle of Man's 30th Lieutenant Governor when he was sworn in on 27 May.
He succeeds Adam Wood who stepped down in April after five years.
Bernard Moffatt, of the Celtic League said the position was a "relic of the colonial past" and "could not be justified."
Sir Richard represented the Isle of Man in Orkney at a commemoration to those who lost their lives at the Battle of Jutland, a key naval engagement of World War One.
He said: "Because of the Isle of Man's strong and heroic maritime and naval history, Government and I thought it right to accept the invitation."
The Lieutenant Governor acts as the representative on the Isle of Man of the Lord of Mann, currently Queen Elizabeth II.
No Manx-born person has ever been appointed to the role.

Residents said that at the height of the flood, about 3ft (1m) of water was lying in parts of the Wester Inch estate, Bathgate.
About 20 homes are thought to have been affected.
A senior Scottish Water official later told 150 local residents at a public meeting that the water main was "absolutely not" fit for purpose.
Chief operating officer Peter Farrer also gave an "unreserved apology" for the incidents.
At the time of the flooding, some of the residents were at a local hotel having a meal paid for by Scottish Water following the previous incident.
The flooding affected homes in Meikle Inch Lane, and supplies to parts of Bathgate, Blackburn and Livingston were disrupted.
The first incident happened on Wednesday when "extensive flooding" closed Meikle Inch Lane and Leyland Road for seven hours. A total of 17 properties were affected.
Resident Mark Snedden told BBC Scotland there was a sense of panic when the rising water was seen.
"We ran out of the house to move our cars to safety based on how high the water had got on Wednesday," he said.
"We then rushed to some of our neighbours' homes, neighbours that had been flooded, to let them know that the water had returned because they were actually walking in their flood-damaged homes."
Scottish Water apologised unreservedly for any inconvenience caused and said it wanted to reassure customers that the company was "committed to gaining a full understanding as to why these bursts have occurred".
A statement said: "We have teams on site in the Meikle Inch Lane area that have isolated the burst and introduced backfeeds into our network.
"This has enabled us to restore normal supplies to the majority of customers who were affected in some parts of Bathgate, Blackburn and Livingston. Water tankers are also available if needed to support the network.
"We have staff on site in the area to help support affected customers and we are liaising with other agencies such as West Lothian Council and the Scottish Fire and Rescue Service."
The statement said incident teams had been working through the night.
"Our main priority is to do everything that we can to help customers affected by flooding and loss of water supply, for some, the second time this week, and to provide the necessary support they require," it added.
"We will also investigate whether we can isolate this section of main whilst maintaining supplies to ensure that there is no repeat of this burst."
Scottish Water representatives addressed a public meeting at Simpson Primary School.
The "huge costs" of having a Lieutenant Governor for the Isle of Man "cannot be justified," a nationalist group said.
[NEXT_CONCEPT]
Homes in West Lothian have been flooded for the second time in four days, after the same water main burst again.