The most common and most likely answer to this crossword clue is the 8 letter word CHAINING
I've seen this crossword clue in The Times
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Buddy explains!

The straight part
We know that "Making fast" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case making fast = chaining.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 CHAINING mean?
CHAINING verb- To fasten something with a chain.
- To link multiple items together.
- To secure someone with fetters.
- To obstruct the mouth of a river etc with a chain.
- To obligate.
- To relate data items with a chain of pointers.
- To be chained to another data item.
- To measure a distance using a 66-foot long chain, as in land surveying.
- (associated with Acorn Computers) To load and automatically run (a program).
- The act or process by which something is chained.