I wrote in an essay: 'We now have licence to move beyond [an idea].' Grammarly flagged this up, saying that I should add an article before 'licence'. Is this true, or is 'licence' interchangeable with 'permission' or 'freedom' in this context?
As usual, Grammerly can not think beyond the literal. Your sentence:
'We now have license to move beyond [an idea].
is correct. From the OED: license
liberty (to do something), leave, permission. Now somewhat rare. †Also occasionally exemption from (something). †Formerly often in licence and leave; by, with, without (a person's) licence; to get, give, have, obtain, take licence.
Your usage implies permission is or has been given.