The most common and most likely answer to this crossword clue is the 8 letter word FATHERLY
I've seen this crossword clue in The Sunday Telegraph
F
A
T
H
E
R
L
Y
More clues leading to the result FATHERLY
Buddy explains!

The straight part
We know that "Like man dealing with issue in caring way" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like man dealing with issue in caring way = fatherly.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 FATHERLY mean?
FATHERLY adjective- Characteristic of what is considered the ideal behaviour pertaining to fatherhood.
- Characteristic of fathers, paternal.