The Scottish Labour MSP, elected just last month in the West Scotland region and appointed the party’s community safety spokesperson, also said a second independence referendum should be held if the Parliament votes for one to take place.
In an interview with the BBC, Ms Clark, who developed a reputation as a rebel during Ed Miliband’s Labour leadership when she was MP for North Ayrshire and Arran, spoke against current Scottish Labour policy on Trident as she mooted a policy on “home rule” for Scotland.
This she said could involve further devolution of powers to Holyrood but while pensions or defence would remain at Westminster, the Scottish Parliament should be consulted on changes to both, and its agreement should be required.
For instance, she said that on the proposed renewal of the UK’s nuclear deterrent, Holyrood should be consulted because "it does directly affect Scotland, Scotland is the base for those nuclear weapon systems, as well as the UK Government having to agree then the Scottish Parliament also should have to consent to those decisions”.
Asked is that would give Holyrood a “veto”, she said: “Effectively yes”.
Pressed on whether that would extend to the system being used in war, she added: “My view is yes.”
The politician, who is a founding member of the Campaign for Socialism, was former Labour leader Jeremy Corbyn’s political secretary. He later made her a life peer, with her title the Baroness of Kilwinning.
Ms Clark also said that while she didn't campaign for a second independence referendum, and doesn't think one should be held “now”, if the Scottish Parliament “should vote for one, if that should happen, if the Scottish Parliament says there needs to be a referendum I would argue that there should be one”.
Scottish Labour leader Anas Sarwar campaigned during the May election for a focus on Covid recovery in the next term of the Scottish Parliament, rather than rerunning constitutional arguments.
The party’s policy on Trident is supportive of renewal of the system, and it supports powers over national security and defence issues being held at Westminster.
A party spokesperson said: "Scottish Labour, and the Labour movement across the UK, is committed to modernising the UK's constitutional settlement so that it works for all of our nations and regions.
"Scottish Labour will continue to advocate for a strong Scottish Parliament."
Scottish Conservative constitution spokesman, Donald Cameron, said it was “absurd” for a “senior figure in Scottish Labour to call for a Holyrood veto over explicitly reserved powers that are clearly UK-wide decisions.”
He added: “This Labour home rule plan risks undermining the foundations of the United Kingdom and our national security.”However SNP MSP Rona Mackay said it was “welcome to see senior Labour figures supporting the right of the Scottish people to decide their own future – rather than have it dictated for us by Westminster governments that we don’t vote for.”