Cold actor picks up cap in military town (7)

I believe the answer is:

chatham

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

'military town' is the definition.
'chatham' can be an answer for 'town' (I've seen this before). I am unsure of the 'military' bit.

'cold actor picks up cap' is the wordplay.
'cold' becomes 'c' (eg on taps).
'actor' becomes 'ham' (ham actor is a kind of actor).
'picks up' is an insertion indicator.
'cap' becomes 'hat' (I've seen this before).
'c'+'ham'='cham'
'cham' going around 'hat' is 'CHATHAM'.

'in' is the link.

Can you help me to learn more?

(Other definitions for chatham that I've seen before include "Former PM" , "Kent ex-dockyard town" , "Town in north Kent" , "Historic Kent dockyard" , "Former naval town in Kent" .)

I've seen this clue in The Sunday Times.

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