Probably named after Clara Holland, daughter of Joseph Holland of Holland House. Like Clara Park, Clara Road, Clara Way and the other streets named Clarawood, this street is located close to the former site of Holland House. According to Ros Davies, Joseph Holland was a stonemason, artist, antique dealer, landlord and landowner of 800 acres of East Belfast. He died in 1900 in Cherryville Cottage, Sandown Rd. Clara died aged 18 in 1899 and is buried in Belfast City Cemetery.
On the recommendation of the assistant city surveyor, the committee approved of the housing and (Clearance and redevelopment) committees naming a new street on their property at Clara Park Estate Clarawood Walk. (15th November 1960).