According to one US diplomat, there are 16 countries currently part of the coalition providing support and training to the Iraqi military, although he did not provide a detailed list of these countries.
if U.S. forces leave Iraq it means almost certainly that the other 16 members of the military coalition that is still helping the Iraqis fight ISIS in training the Iraqi Army will also leave.
A bit more googling found an older (2016) article listing 16 countries... the list includes Iran and Russia though, so maybe all of them leaving is a bit of exaggeration... Some excerpts for the NATO & Western countries (omitting aircraft info):
Up to 350 British soldiers and advisers are deployed in Iraq, centred in Erbil and Nineveh. Their role is limited to training as well as logistical and aerial support for the Iraqi army and Kurdish Peshmerga forces.
Around 200 Australian special forces are present in the Kurdistan region, overseeing training, support and electronic surveillance of IS.
Belgium deploys 120 soldiers and trainers in a camp near the Jordanian border with Iraq as well as in Kurdistan. They provide support and surveillance to anti-IS operations in northern Iraq.
Up to 700 Canadian military personnel are present in Baghdad and Erbil, providing training, support and reconnaissance.
Denmark: The Scandinavian nation has 140 military mostly non-combat personnel in advisory and training capacities. They are present in a small base shared with the Peshmerga southwest of Erbil.
Around 500 French military personnel are present in Iraq as part of the special forces unit. Most of them are serving in a support capacity, including analysts working with images provided by fifteen French reconnaissance planes operating over Iraq and Syria.
Berlin maintains 150 military personnel mostly officers, part of a newly formed European anti-terror unit, based between Baghdad and Erbil. Germany also runs a training camp for Kurdish volunteers and fighters, with focus on programmes related to use of European weapons supplied to Iraq, mostly Kurdistan. Germany is part of the international coalition.
Rome dispatched 450 military personnel to Iraq amid warnings of the collapse of a dam in Mosul.
Around 150 Dutch soldiers are training Iraqi soldiers in northern Iraq.
Turkey has contributed nearly 600 troops, tasked with training Kurdish forces and Mosul tribes to fight IS and force it out of the city, as well as protecting borders from PKK infiltration. It has weapons and armoured vehicles to defend its camp in Bashiqa, 30 kilometres northeast of Mosul.
Sweden: Forty advisers working with the army.
Norway: Unknown number of trainers in Baghdad.
Spain: A few dozen trainers working with the Iraqi army and local police in Baghdad and northern Iraq.
I don't know how up-to-date that list is for 2020.
Of note however is that NATO has an official mission in Iraq; from its official page:
At the Brussels Summit in July 2018, NATO leaders agreed to launch NATO Mission Iraq (NMI), on the request of Iraq.
NMI is a non-combat training and capacity-building mission, conducted with full respect of Iraq's sovereignty and territorial integrity.
It was established in Baghdad in October 2018 and involves around 500 trainers, advisors and supporting personnel from Allied and partner countries, including Australia, Sweden and Finland.