The co-leader of the Social Democrats says there are still major outstanding questions that Davy and the Central Bank need to answer.
The stockbroker's chief executive and two other senior figures have resigned over their involvement in a 2014 bond deal.
The firm says all three offered to step down after it was fined €4.1m by the Central Bank for breaches of market rules.
An investigation was started after a group of 16 staff members engaged in a personal transaction with a client in November 2014.
There have since been calls for those employees, who bought a client's Anglo Irish Bank bond instead of offering it on the open market, to be personally sanctioned.
The Social Democrats' Róisín Shortall has since written a letter to the Governor of the Central Bank outlining ten questions that she believes remain unanswered about the issue.
Speaking to On the Record with Gavan Reilly, she outlined some of those queries she hopes will be thoroughly addressed.
"I was wondering, what about the 16 individuals themselves, what happened to the money that was made in that transaction," she said.
"Is it the intention to name those 16 individuals, we know maybe five have been named already but what about the rest of them?
She has also questioned the company's relationship with the NTMA, and how appropriate it is for Davy to continue to operate the Irish Stock Exchange.
With regard to the fine levelled on the company, Ms Shortall added it was important to understand the size of the financial penalty relative to Davy's overall turnover.
"€4m, while it seems like a lot of money, really amounts to a slap on the wrist and it's imposed on the company itself," she said.
"What about the individuals, what about bringing them to book?
"And another question I asked was, in relation to the activity the 16 were involved in, was that actually criminal activity in 2014 when the behaviour occurred and is it currently criminal activity?
"How up to date is our fraud legislation and our company law at the moment?"
The Davy 16 must be made personally accountable for their behaviour. Also need for full accountability from Davy itself, where there has been a catastrophic failure of internal checks, including their compliance department and audit. https://t.co/9f7MgJn8Hm
— Róisín Shortall (@RoisinShortall) March 6, 2021
Ms Shortall said she is hopeful the Governor of the Central Bank will get back to her with comprehensive answers.
"I think it is quite sickening for the public listening to this yet again of a financial institution engaging in impropriety and behaviour that is certainly unbecoming of a major financial institution," she continued.
"There can be no question of a line being drawn under it after three people resigned yesterday, there's a lot of outstanding questions that must be dealt with."
In order for a sense of justice to be achieved, Ms Shortall added that it is "imperative that those who breach the rules, to say the least, need to be seen to be made accountable".
The Central Bank are due to appear before the Oireachtas Committee on Finance, Public Expenditure and Reform on Tuesday.
Ms Shortall stated that the regulator needs to explain why it took so long to take action with Davy.
"The €4m is only one very small part of it, the three people resigning yesterday is only one small step," she said.
"But there are major outstanding questions that need to be answered both by Davy and the Central Bank.
"The sooner we get those answers, the better."
