Complex sentence: Six years later he was chosen to be an assistant-physician to the Brompton Hospital for Diseases of the Chest, and with that institution he retained his connection until his death, first as full (1855), and subsequently as consulting physician (1875).
Split into simpler sentences: Six years later he was chosen to be an assistant-physician to the Brompton Hospital for Diseases of the Chest. He retained his connection with that institution until his death, first as full physician (1855), and subsequently as consulting physician (1875).