The most common and most likely answer to this crossword clue is the 3 plus 3 plus 5 letter word OUT AND ABOUT
I've seen this crossword clue in The Daily Telegraph
O
U
T
A
N
D
A
B
O
U
T
More clues leading to the result OUT AND ABOUT
Buddy explains!

The straight part
We know that "Convalescent" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case convalescent = out and about.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.