lay in a good stock of mothproofers which contain Transfluthrin, and of large, clear plastic bags. Or you can use those plastic storage crates with tight-fitting lids. These will be handy for packing stuff before the move, and in transit, and you need not unpack them until needed.
The mothproofers are mostly sized to treat a half-cubic metre of space (read the packaging)
you can kills moths, eggs and larvae with a hot wash or tumbledrier. Put all the clothes immediately in a bag or crate with a mothkiller, and seal it, to prevent reinfestation. You can leave out-if-season clothes and spare bedding sealed up like that to prevent them being attacked in storage.
That will prevent the clothes bringing moths with them.
You will have to put mothkillers in all your wardrobes and drawers in the new house, after cleaning them. Hoovering carpets, especially round the skirting boards and under furniture where they like to lurk, will reduce their numbers. You may need to spray in these places, after cleaning.
Cedar and lavender make moths smell nice but do not kill them.