Fruit with a soft cheese: no thanks! (7)
I believe the answer is:
apricot
'fruit' is the definition.
(type of fruit)
'a soft cheese no thanks' is the wordplay.
'soft' becomes 'p' (musical abbreviation for piano, 'soft').
'cheese' becomes 'ricotta' (ricotta is a type of cheese).
'no' indicates named letters should be taken away.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'ricotta' with 'ta' taken out is 'ricot'.
'a'+'p'+'ricot'='APRICOT'
'with' is the link.
(Other definitions for apricot that I've seen before include "Fruit from a tropic" , "Small, peach-like fruit" , "Stoned fruit" , "Orange fruit" , "Soft, peach-like fruit" .)