I own a travel agency. I have recently taken on an independent agent to whom I pay a portion of commissions earned to. How do I report their earnings (and mine)?

Do you file Schedule C to report your 1099NEC self employment income?  You will give the independent agent a 1099NEC for their part.  You can expense it on your return under Contract Labor on Schedule C.   I don’t know where you report it if you need to file a separate business return for your travel agency.