Company running O365 and on prem Active Directoy is splitting and new company wants to run Azure AD

My company currently uses O365 and we sync our AD from on premises to Azure. This company is branching off and forming a new company. I am looking for help on how to get this new company running Azure AD only, (they will have O365 as well) and more specifically how do I get that domain to do a trust with my on premises domain? Ex: current company is abc.com running AD onsite and using O365, new company xyz.com spinning off from abc.com, will not have on premise AD instead will use Azure AD and I need abc.com to trust the Azure AD domain xyz.com