Hospital with new antigens for fast-tracking (9)

I believe the answer is:

hastening

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'fast-tracking' is the definition.
I can't judge whether this defines the answer.

'hospital with new antigens' is the wordplay.
'hospital' becomes 'H' (abbreviation for hospital).
'with' says to put letters next to each other.
'new' is an anagram indicator.
'antigens' is an anagram of 'astening'.
'h'+'astening'='HASTENING'

'for' acts as a link.

Can you help me to learn more?

(Other definitions for hastening that I've seen before include "Accelerating, expediting" , "Hurrying, rushing" , "Hurrying along" .)

I've seen this clue in The Sunday Times and The Times.

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