I presume that you found my previous posts on this issue thanks to
@Sue Ellen's links etc.?
You have to wait until your current service finishes and your final bill is issued which should be on or about 28th June. Once that happens you are no longer a customer and should be able to sign up as a new customer online and avail of the preferential new customer deals. At least that's worked for me for the past few years and I'm hoping that it still works as I'll be trying it again myself in a couple of months in order to get a new customer deal for another 12 months.
I've seen some people on the links of Boards and Reddit talking about using different personal details (partner's/house sharer's details, different email address, different phone number etc.) but I never found that to be necessary. I just signed up again using my usual personal details.
Edit: just read
@skrooge's post above and maybe signing up using someone else's details (e.g. partner) is a way to avoid any downtime altogether. That wasn't an option for me and, in any case, a few days on 4G didn't bother me unduly. But some users may not have that flexibility.
As mentioned elsewhere, for the few days that I was ever offline from proper broadband I used a spare 4G router and 48 SIM (€12.99/200GB per month) as a temporary stopgap.