Cycle is a code statement used in loops to return to the top of the loop.
NetTalk apps are written in clarion, so Cycle works just like before - you don't need to change it at all - it jumps to the top of the loop.
I suspect you are referring to the CYCLE statement used to "swallow" a windows event - assuming you still use that Legacy-based tradition, but given that the WebProcedures have neither an ACCEPT loop, nor Windows events, I'm not sure what you are trying to accomplish.
You'd probably be better off framing the question around the problem you are actually trying to solve, rather than looking for some equivalent of how you might solve the problem using some other architecture.
cheers
Bruce