The retune usually has a period of a few weeks where both the old and new channel frequencies are broadcasting. So you should either be able to retune now, or will have a few weeks after June 10th before the old frequencies get switched off.
Depending on your recorder it may handle it all automatically. On Beyonwiz and Humax PVRs you can disable the Dynamic Channel Update but by default it is enabled, which will allow them to automatically update the channels to the new frequencies. As you view a channel from each network that network's channels get automatically updated to the new frequency.
If your recorder does not update the channels automatically you just need to do an auto tune, then 'Resend all recordings' from 'My Account > My Recorders' on the website.
Note: If you do an auto tune on a Topfield (though you shouldn't need to) you should 'clear services' first, and then after the auto tune you will need to re-enable IceTV and re-enter your IceTV account details on the Topfield - before resending all recordings.
If you are in an area where your recorder usually picks up 2 sets of channels, requiring manual effort to remove the weaker duplicates, you may be better off contacting IceTV support before doing anything - unless you know what you are doing.
