That would depend primarily on operational project imperatives and systems.
If you work in an Agile environment, then you should budget and plan the next functional requirements as an incremental improvement to the one you already committed to build.
Other environments still allow for a planned rollout of improvements after the first deliveries are released. Is it a viable experience? Then you have an MVP to present, followed by an iteration(s) plan with your new discovered components.
It’s never a good idea to stop and re-start every time you find something new to add to the scope.
Unless absolutely necessary (meaning, unless user value is compromised) you should treat any newly discovered functional - and non-functional - requirements as things to iterate upon next.
This will keep your budget, resource allocation, capability, plans and colleagues at pace and without the added stress.
PS: if you’re a sole trader / consultant, you are likely going to need to bite that bullet and present a viable scope to your client. You don’t want to commission incomplete work that is likely to result in a poor experience. Ultimately, in this case, we are accountable for as thorough and functional a discovery and requirements plan as possible.
I hope that helps.
All the best.