Rather early to be lifting for storage yet, right now just pull what you need. Lift in late September early October clean off any soil, check for root fly damage and, if you find any, do not try to store those carrots. You can store in a sand clamp or a pit lined with straw. I've even heard of folk using an old washing machine drum sunk in the ground to store carrots in. Alternatively keep them well covered with straw and fleece to hold the straw down and leave in the ground. So long as they don't get frozen they will be fine.

Wish our carrots had done well enough that we had some to store!