Complex sentence: After his discharge from the military in 1947, he began to play at local venues in Phoenix, then moved on to host his own show on KTYL and then his own television show on KPHO-TV in Phoenix.
Split into simpler sentences: After his discharge from the military in 1947, he began to play at local venues in Phoenix, then moved on to host his own show on KTYL. He thereafter had his own television show on KPHO-TV in Phoenix.