The most common and most likely answer to this crossword clue is the 10 letter word WATCHSTRAP
I've seen this crossword clue in The Times
W
A
T
C
H
S
T
R
A
P
Buddy explains!
The straight part
We know that "What’s near to hand, fixing the time?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what’s near to hand, fixing the time? = watchstrap.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.