The most common and most likely answer to this crossword clue is the 5 letter word LIMIT
I've seen this crossword clue in The Times
L
I
M
I
T
More clues leading to the result LIMIT
- Bound books concealing note
- Yours truly’s following lake north of Italian border
- Maximum speed came down, motorway included
- Bound to be fired after penning note
- End of motorway having illumination all round
- Ceiling clearly visible, 100cm obscured
- Tramp’s wearing tight cap
- Check literature about married setter
- I will chase after lecturer’s cap
- Maybe borderline books with note written in
Buddy explains!

The straight part
We know that "border" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case border = limit.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 LIMIT mean?
LIMIT noun- A restriction; a bound beyond which one may not go.
- A value to which a sequence converges. Equivalently, the common value of the upper limit and the lower limit of a sequence: if the upper and lower limits are different, then the sequence has no limit (i.e., does not converge).
- Any of several abstractions of this concept of limit.
- The cone of a diagram through which any other cone of that same diagram can factor uniquely.
- Fixed limit.
- The final, utmost, or furthest point; the border or edge.
- The space or thing defined by limits.
- That which terminates a period of time; hence, the period itself; the full time or extent.
- A restriction; a check or curb; a hindrance.
- A determining feature; a distinguishing characteristic.
- The first group of riders to depart in a handicap race.
- (as "the limit") A person who is exasperating, intolerable, astounding, etc.
- Being a fixed limit game.
- To restrict; not to allow to go beyond a certain bound, to set boundaries.
- To have a limit in a particular set.
- To beg, or to exercise functions, within a certain limited region.