Crossword Genius

Liquid carrier's first thing needed for big run (7)

Ross

I believe the answer is:

bladder

I'm a little stuck... Click here to teach me more about this clue!

'liquid carrier's first thing needed' is the definition.
I can't tell whether this defines the answer.

'big run' is the wordplay.
'big' becomes 'b' (I can't justify this - if you can you should believe this answer much more).
'run' becomes 'ladder' (both can mean a rip in tights).
'b'+'ladder'='BLADDER'

'for' is the link.

Can you help me to learn more?

(Other definitions for bladder that I've seen before include "Bag in the lower abdomen" , "Distensible sac" , "Chamber" , "organ" , "may be subject to inflation?" .)

I've seen this clue in The Times.
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