The most common and most likely answer to this crossword clue is the 4 letter word DRIP
I've seen this crossword clue in The Times
D
R
I
P
More clues leading to the result DRIP
- Daughter, not fully mature, weak character
- Swim across river? One's rather wet
- Make a slow escape, taking irrational road westward
- Continually supply daughters, after putting in opening payment
- Fool runs into the clutches of pickpocket
- Swim across river, feeble one!
- Daughter takes rent for weed
- Medic with very little cash for drug supplier
- Wimp finally shed tear
- Plop tips of dried rosemary into pan
Buddy explains!

The straight part
We know that "Make a slow escape" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make a slow escape = drip.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 DRIP mean?
DRIP verb- To fall one drop at a time.
- To leak slowly.
- To let fall in drops.
- (usually with with) To have a superabundance of valuable things.
- (of the weather) To rain lightly.
- To be wet, to be soaked.
- To whine or complain consistently; to grumble.
- A drop of a liquid.
- A falling or letting fall in drops; act of dripping.
- An apparatus that slowly releases a liquid, especially one that intravenously releases drugs into a patient's bloodstream.
- A limp, ineffectual, or uninteresting person.
- That part of a cornice, sill course, or other horizontal member, which projects beyond the rest, and has a section designed to throw off rainwater.
- A dividend reinvestment program; a type of financial investing.