The most common and most likely answer to this crossword clue is the 9 letter word RECOMMEND
I've seen this crossword clue in The Daily Telegraph
R
E
C
O
M
M
E
N
D
More clues leading to the result RECOMMEND
Buddy explains!

The straight part
We know that "Suggest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suggest = recommend.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.
What does RECOMMEND mean?
RECOMMEND verb- To bestow commendation on; to represent favourably; to suggest, endorse or encourage as an appropriate choice.
- To make acceptable; to attract favor to.
- To advise, propose, counsel favorably
- To commit, confide to another's care, confidence or acceptance, with favoring representations