The house was built for Thomas Tyndall KCB, in the 18th century, on the site of bastions which were fought over during the English Civil War and demolished in 1655.
The building currently houses the University of Bristol's Faculty of Science offices, the Brigstow Institute, Elizabeth Blackwell Institute for Health Research, the Cabot Institute and the Jean Golding Institute for data-intensive research.
This isn't Park Street but Queen's Road. The building in scaffolding is the Wills Memorial Tower, Bristol University see ST5873 : The Wills Memorial Tower Under Repair. Park Street doesn't start until you turn right to go down the hill, by the light green painted shop just out of shadow on the right. (Fondly remembered from my days as a student in Bristol - the Bekeley Cafe is in shadow on the right, blue neon sign is just legible).