The most common and most likely answer to this crossword clue is the 3 letter word HUG
I've seen this crossword clue in The Times
H
U
G
Buddy explains!
The straight part
We know that "Closely follow" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case closely follow = hug.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 HUG mean?
HUG noun- A close embrace, especially when charged with such an emotion as represented by: affection, joy, relief, lust, anger, agression, compassion, and the like, as opposed to being characterized by formality, equivocation or ambivalence (a half-embrace or "little hug").
- A particular grip in wrestling.
- To crouch; huddle as with cold.
- To cling closely together.
- To embrace by holding closely, especially in the arms.
- To stay close to (the shore etc.)
- To hold fast; to cling to; to cherish.