Rush to have surgery on neck (6)

I believe the answer is:

gallop

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'rush' is the definition.
(thesaurus)

'surgery on neck' is the wordplay.
'surgery' becomes 'op' (short for operation).
'on' is a charade indicator (letters next to each other).
'neck' becomes 'gall' (I can't justify this - if you can you should give a lot more credence to this answer).
'op' put after 'gall' is 'GALLOP'.

'to have' is the link.

Can you help me to learn more?

(Other definitions for gallop that I've seen before include "Horse-exercising track" , "Horse's gait" , "All at GPO can go at this rate" , "Fastest gait of a horse" , "Hurry (on horseback?)" .)

I've seen this clue in The Sun.

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