The Standards in Public Office Commission has called for more powers under the Regulation of Lobbying Act 2015.
A new report by the commission shows that a former public official was the first known person to breach lobbying laws by engaging in lobbying less than a year after leaving the job.
Under the legislation, certain officials who leave their post are subject to a one year "cooling off" period.
Head of Ethics and Lobbying Regulation with the Commission Sherry Perreault said the commission does not have the authority to investigate or prosecute breaches of the act's post-employment provisions.
"We are calling on the Government to amend the act to provide the commission with powers to investigate and prosecute such breaches," she added.
Ms Perreault said this would mean it would be an offence for someone to lobby their former employer or colleagues until one year after they left the Government.
The commission's report says lobbying is becoming increasingly transparent and the public can see more easily who is seeking to influence decision-making.
The report found that health is the area most lobbied about, followed by economic development and industry.
A new register aimed at those engaged in lobbying has had 1,869 organisations sign up.
It requires anyone involved in lobbying to record details, including names of public officials contacted, subject matter and the intended results.
Members of the public can inspect the register that will show which TDs, ministers, councillors and public officials have been lobbied.
The report shows that in 2018 almost 10,000 returns of lobbying activities were submitted.
The commission says a public consultation process on the second legislative review of the act, led by the Minister of Public Expenditure and Reform, is ongoing.