One new hair product gives heavenly body! (5)
I believe the answer is:
angel
'heavenly body' is the definition.
(I've seen this in another clue)
'one new hair product' is the wordplay.
'one' becomes 'a' (a thing is one thing).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'hair product' becomes 'gel' (hair gel).
'a'+'n'+'gel'='ANGEL'
'gives' is the link.
(Other definitions for angel that I've seen before include "local to Islington" , "Theatrical backer" , "Theatre financier" , "Ministering spirit" , "Sponsor" .)