Singer has one foundation (5)
I believe the answer is:
basis
'foundation' is the definition.
(I know that foundation can be written as basis)
'singer has one' is the wordplay.
'singer' becomes 'bass' (bass is a kind of singer).
'has' indicates putting letters inside.
'one' becomes 'I' (Roman numeral).
'bass' going around 'i' is 'BASIS'.
(Other definitions for basis that I've seen before include "First principle" , "Foundation, fundament" , "Fundamental part" , "Principal element" , "Underlying support for a theory" .)