How to add new content using a content type added after taxonomy access control was installed?
Have a look at the Community documentation of the Taxonomy Access Control module. Especially what it says about the Global default (within Global and vocabulary defaults), i.e:


  The global default, at the top of the form, determines the grants the role receives for untagged nodes (including nodes with terms that are not in controlled vocabularies). Keep in mind that access is denied by default, so if you want TAC to grant a role access to untagged nodes, set the global default to allow for that grant and role.


See what happens if you adapt this default. If the issue persists, then you may want to perform TAC troubelshooting, possibly even Troubleshooting with Devel.