According to Historic England, Terrace House was built in the early to mid 19th century.
The tithe map for Ashburton, drawn circa 1840, shows two small buildings close to where Terrace House is now, but nothing that seems large enough for a dwelling.
https://historicengland.org.uk/listing/the-list/list-entry/1207744?section=official-list-entry - accessed 19-03-2022 https://www.devon.gov.uk/historicenvironment/tithe-map/ashburton/ - accessed 17-03-2022
The number on the tithe map is 957, adjoining 958 further along Rew Road. The land opposite is 959. John Luscombe is shown as both the owner and occupier of 957 and 958.
How this fits with Terrace House being part of Lord Clinton's estate in 1905 (below) I do not know.
https://devoncc.sharepoint.com/sites/PublicDocs/Environment/Historic/Tithe%20Apportionment%20Transcriptions/PDF/ashburton.pdf?ga=1 - accessed 15-04-2022
In the 1841 census John Luscombe, aged about 40, was in the first property in North Street. A wheelwright, he was living with [his wife] Elizabeth, and a two year old girl, Susan.
The family may have been living at Terrace House; the building opposite is later, and possibly at the time, a wheelwright's shop.
1841 census HO107, piece no. 253, folio 3, p1
By 1851 John was, in addition to being a wheelwright, an innkeeper. He was still in North Street with his wife Elizabeth and two daughters, but there are properties either side of where they were living.
He was still an innkeeper in 1861, and in this census the inn was named as the Victoria.
1851 census HO107, piece no 1871, folio 328, p31
1861 census RG09, piece no 1405, folio 58, p25