The EU is a perfect example. A significant number of EU countries have proposed that a free trade agreement with a third party be suspended. A state can suspend the entire agreement, not just the environmental chapter, when the other party fails to uphold its obligations under the nationally determined contributions in the Paris agreement.
Those discussions are already under way. I think suspension would be a last resort, but many other measures ranging from the option you proposed to suspension can be taken to ensure that both parties commit to honouring their commitments and to making their targets under the agreement much more ambitious.