The Tory MEP said such trade and criminal activity has a value of between €8bn and €20bn a year.
The deputy's demand for a clampdown comes as new figures estimate the number of African elephants has fallen by a third in the last seven years.
Separately, there were fresh calls this week from animal welfare groups to halt the "cruel" trade in elephant ivory and rhino horn.
The EU is the world's largest exporter of pre-convention ivory - ivory acquired before the entry into force of the Convention on International Trade in Endangered Species (CITES) in 1975.
Between 2011 and 2014, member states reported seizures of around 4500 ivory items reported as specimens and an additional 780 kg as reported by weight. Between 2003 and 2014, 92 per cent of EU exports of pre-convention tusks went to China or Hong
McClarkin's report proposing how international trade agreements could be used to combat wildlife trafficking will be introduced in December.
The report will, she said, identify ways of formulating trade policies to tackle the illicit trade in wildlife and wildlife products that is largely to blame for the rapid decline.
It will also call for improved use of customs technology at all stages of the supply chain and the need for an international response to ensure the EU is in step with the World Trade Organisation and CITES.
McClarkin, the Conservative party's international trade spokesperson, spoke about her proposals during a debate on the EU's separate wildlife trafficking action plan.
The ECR group deputy told members of Parliament's international trade committee this week that the world was experiencing an unparalleled surge in the illegal trade of wildlife and wildlife products which threatened to overturn decades of hard won conservation gains.
"The illicit wildlife trade does not only have a devastating effect on its biodiversity, but it has a detrimental impact on the development of the rule of law and of good governance.
"Combined together these problems can lead to a very dangerous destabilisation of the security in affected nations.
She added: "It is not just about environmental protection but also about cutting off a source of financing for the corrupt and the criminal."
The EU's action plan takes a broad and linked-up approach to developing a continental response to wildlife trafficking. McClarkin's report will look further in detail at how specifically the formulation of international trade policy could help in this battle and what technical mechanisms might be introduced to take on the illegal trade.
The parties to the Convention on the International Trade in Endangered Species of Wild Fauna and Flora (CITES) will meet in Johannesburg later this month to discuss the broad issue of wildlife trafficking, including the trade in ivory which came under the spotlight this week.
Ivory is prized for a variety of reasons. In Japan it is used to make family seals; in the Philippines it is used for religious artefacts. Campaigners said elephants would be protected only if all nations observed a domestic ban.
Experts say a ban on trade in ivory, including in all EU member states, is urgently needed. There are about 450,000 African elephants left, but 30,000 a year are being slaughtered.
A large number of African nations have promised to outlaw domestic ivory markets, while France, the US and, crucially, China have introduced their own bans or are in the process of doing so.