The most common and most likely answer to this crossword clue is the 16 letter word TEAÂ ANDÂ SYMPATHY
I've seen this crossword clue in The Guardian
T
E
A
Â
A
N
D
Â
S
Y
M
P
A
T
H
Y
Buddy explains!

The straight part
We know that "Support" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case support = tea and sympathy.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.