The most common and most likely answer to this crossword clue is the 5 plus 3 plus 5 letter word CARRY THE TORCH
I've seen this crossword clue in The Daily Telegraph
C
A
R
R
Y
T
H
E
T
O
R
C
H
More clues leading to the result CARRY THE TORCH
Buddy explains!
The straight part
We know that "Suffer from unrequited lov/offer some illumination" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suffer from unrequited lov/offer some illumination = carry the torch.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.