is it possible to use start event again after an end event was declared in BPMN?

i'm new in BPMN, i have a problem in BPMN where a pool lane is already decleared it's Start Event and went idling for long time. So is it okay to give an End Event then use the Start Event again when it have new task? i gave the example below sorry for my bad english thank you

The short answer is no.

It is normal for the process to idle, sometimes even for a long time. That's what intermediate events are for. The flow will wait for the event to happen, as long as it needs to. It also opens a possibility to handle the exception handling when the idle/waiting time is too long.

It is also important to understand that there is no single way of splitting what a complete process is. In one company (or e.g. from department perspective), the process of accepting an invoice will end as soon as it has been sent to accounting. The later handling of the payment (once the booking is invoiced) can be considered a second process. But in such case, those two separate processes will be depicted on two separate diagrams. For other company, the process starts when the invoice has arrived and lasts until no-one has to touch the same invoice again (i.e. it's paid and closed by the accounting team). Then you have a single process and whenever you are waiting for other departments/process counterparts, you just use the intermediate events and indeed go into idle state in the process itself.

BTW, the start/end events are per pool, not lane. The process can go across different lanes within the same pool (typical, when more participants in the considered organisation are involved). It can also communicate with other pools through messages and then wait for the response.