Is there a way to create a TREC contract in Podio? i.e. have a TREC template that I can have auto filled out by clicking “create contract”
Sure you can, and there are probably a few ways you can do it. The best way would be with a template like you said. You can build in merge fields into the template and it should work pretty good. One such service that would work for your is Webmerge.
Podio has a Webmerge extension that should make the process fairly easy to setup. The only issue is cost per month as it will be $29/mo for 30 merges and 3 templates.
There are ways to do it for free using Globiflow and HTML to create the template. See my tutorial on creating offer letters, it would be the same concepts. Only issue here is that it is sometimes tricky (or impossible) to get the exact format you might want.
Hope that helps,