Person bagging degree, Cambridge's ultimate blue (7)
I believe the answer is:
obscene
'blue' is the definition.
(blue can mean pornographic)
'person bagging degree cambridge's ultimate' is the wordplay.
'person' becomes 'one' ('one' can mean an unspecified person).
'bagging' indicates putting letters inside (bag can mean to obtain or contain).
'degree' becomes 'bsc' (Bachelor of Science degree).
'ultimate' indicates one should take the final letters (the last or ultimate letter).
The last letter of 'cambridge' is 'e'.
'bsc'+'e'='bsce'
'one' placed around 'bsce' is 'OBSCENE'.
(Other definitions for obscene that I've seen before include "repellent" , "Highly offensive" , "Sexually offensive" , "Lewd or loathsome" , "Morally offensive, disgusting" .)