Hi Shikha, You can reach Leh from Spiti via Keylong. This is the route if you are starting from Delhi: Delhi - Narkanda - Sangla - Kalpa - Nako - Kaza - Chandra tal - Keylong - Leh.
From Keylong, which is the administrative centre of Lahaul and Spiti district, its a 9-10 hour drive spanning 350km wherein you will cross the second highest pass of Tanglang La, Moore Plains, Pang and the Sarchu Gata Loops, to reach Leh in the evening.