There's peel and a pip, unfortunately, in this dessert (5-3)
I believe the answer is:
apple-pie
'this dessert' is the definition.
(I have seen 'Common dessert ' mean 'apple-pie' so perhaps 'dessert' could also mean 'apple-pie')
'there's peel and a pip unfortunately' is the wordplay.
'there's' says to put letters next to each other.
'and' says to put letters next to each other.
'unfortunately' indicates an anagram (a bad or unfortunate spelling).
'peel'+'a'='peela'
'peela' put next to 'pip' is 'peelapip'.
'peelapip' with letters rearranged gives 'APPLE-PIE'.
'in' is the link.
(Other definitions for apple-pie that I've seen before include "Sweet (in good order?)" , "Perfect order -- bed jokily made" , "(Characteristically American) sweet" , "Popular dessert" , "Dish - order - bed" .)