The most common and most likely answer to this crossword clue is the 4 letter word CARK
C
A
R
K
More clues leading to the result CARK
Buddy explains!

The straight part
We know that "Care for the old" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case care for the old = cark.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 CARK mean?
CARK noun- A noxious or corroding worry.
- The state of being filled with worry.
- To be filled with worry, solicitude, or troubles.
- To bring worry, vexation, or anxiety.
- To labor anxiously.
- To drive oakum into the seams of a ship's wooden deck or hull to make it watertight.
- To apply caulking to joints, cracks, or a juncture of different materials.
- Fuck
- See cark it.