The most common and most likely answer to this crossword clue is the 6 plus 7 letter word CORPUS CHRISTI
I've seen this crossword clue in The Daily Telegraph
C
O
R
P
U
S
C
H
R
I
S
T
I
More clues leading to the result CORPUS CHRISTI
- Body of people with crime writer detailed to tour university college
- Rozzer has run inside: crime writer almost catching us in college
- This circus somehow gets backing for a festival
- Police officer collecting King, US novelist heard in college
- and 23: Former sprinter tailed after body found in Cambridge college
- Oxford college’s rustic porch is vandalised
- My drink’s knocked over by Olympic sprinter in audience for festival
Buddy explains!
The straight part
We know that "Cambridge college" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cambridge college = corpus christi.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.