Shop kept by communist given back (8)
I believe the answer is:
restored
'given back' is the definition.
('restore' can be a synonym of 'give back')
'shop kept by communist' is the wordplay.
'shop' becomes 'store' (synonyms).
'kept by' is an insertion indicator.
'communist' becomes 'red' (red can informally mean communist).
'store' put within 'red' is 'RESTORED'.
(Other definitions for restored that I've seen before include "mended?" , "touched up?" , "Returned to original condition or place" , "Refurbished" , "King Charles was" .)