In the event a late fee is not authorized in a declaration, both the Condo Act and the Community Association Act authorize associations to adopt a rule imposing a charge for a late payment of an assessment.  See Utah Code Subsections 57-8-8.1(5)(c) and 57-8a-218(13)(c).   

An association has a lien on a unit or lot for late fees, as well.  See Utah Code Subsections 57-8-44(1)(a)(ii)(B) and 57-8a-301(1)(a)(ii)(B).