The most common and most likely answer to this crossword clue is the 7 letter word CHASING
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result CHASING
Buddy explains!
The straight part
We know that "Running after" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case running after = chasing.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 CHASING mean?
CHASING verb- To pursue.
- To consume another beverage immediately after drinking hard liquor, typically something better tasting or less harsh such as soda or beer; to use a drink as a chaser
- To attempt to win by scoring the required number of runs in the final innings.
- To swing at a pitch outside of the strike zone, typically an outside pitch
- To produce enough offense to cause the pitcher to be removed
- To groove; indent.
- To place piping or wiring in a groove encased within a wall or floor, or in a hidden space encased by a wall.
- To cut (the thread of a screw).
- To decorate (metal) by engraving or embossing.
- Engraved or embossed decoration.