Sings about Hampshire (6)
I believe the answer is:
chants
'sings' is the definition.
(chanting is a kind of singing)
'about hampshire' is the wordplay.
'about' becomes 'c' (abbreviation for 'circa').
'hampshire' becomes 'hants' (postal abbreviation).
'c'+'hants'='CHANTS'
(Other definitions for chants that I've seen before include "Sings in monotone, say psalms" , "Sings in one tone" , "Speaks or sings on a single note" , "Sings monotonously like monks at prayer" , "Snatch (anag)" .)