Former SNP leader, Alex Salmond, said his party had secured time on Thursday to question the government over issues raised by a Royal naval submariner.
William McNeilly went on the run after alleging the missile programme was a "disaster waiting to happen". He later handed himself in to police.
Mr Salmond said the Ministry of Defence must provide detailed answers.
An official investigation was launched after Able Seaman Mr McNeilly, 25, from Belfast, raised his safety concerns in an internet post.
His 18-page report, called The Secret Nuclear Threat, claimed to detail "serious security and safety breaches".
The Navy said the fleet, which is based at Faslane on the Clyde, operated "under the most stringent safety regime".
The MoD said Mr McNeilly was "apprehended" by Royal Navy Police at Edinburgh Airport on Monday night and was being held at a military establishment in Scotland.
The SNP's adjournment debate - called "Safety at HM Naval Base Clyde" - will take place next Thursday.
Mr Salmond, the party's foreign affairs spokesman at Westminster, said: "The SNP will continue to keep the pressure on the government until we are satisfied that not only have they have investigated Mr. McNeilly's claims thoroughly and have acted on the findings but that those findings are put into the public domain.
"Trident is a key issue for people in Scotland.
"It is bad enough that Scotland is forced to house these weapons of mass destruction but these alleged breaches of security are deeply worrying - there must be absolutely no complacency."
Earlier this week a Navy spokesman said: "The naval service operates its submarine fleet under the most stringent safety regime and submarines do not go to sea unless they are completely safe to do so."
He said the Navy "completely disagreed" with Mr McNeilly's report, claiming that it "contains a number of subjective and unsubstantiated personal views, made by a very junior sailor".
However, the spokesman added that it was "right" that the contents of the document were considered in detail.
The safety of the Trident nuclear weapons system is to be debated in the House of Commons next week.