xiǎn means few or seldom and is mostly literary: 鲜为人知 (little-known), 鲜少 (rarely), 屡见不鲜 (a common sight; note this set phrase keeps xiān). The same xiǎn reading is the 鲜 in the place name 朝鲜 (Korea).
Left fish radical, the indexing radical, a side view of a fish. It anchors 鲜 in the aquatic family with 鲤, 鲨, and 鱿. Original sense: a just-caught fish whose flesh has not begun to spoil, the prototype of all fresh food.
Right side 羊 is a goat head with curved horns. Fish plus lamb is a classic meaning compound: the two prized meats of ancient China, both best eaten fresh. The pairing gives 鲜 its core senses of fresh, delicious, and vivid.