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Cold War escalation with gun runners? (4,4)

Ross

I believe the answer is:

arms race

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

'cold war escalation' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.

'gun runners?' is the wordplay.
I cannot quite understand how this works, but
'gun' could be 'arm' (I've seen this in other clues) and 'arm' is present in the answer.
This may be the basis of clue (or it may be nonsense).

'with' is the link.

Can you help me to learn more?

(Other definitions for arms race that I've seen before include "Weaponry competition" , "rush to war" , "dangerous situation escalating" , "A hostile international competition" , "International competition for weapons" .)

I've seen this clue in The Sun and The Telegraph.
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