Make a speedy apology? (7,6)

I believe the answer is:

express regret

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'make a' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'speedy apology?' is the wordplay.
'speedy' becomes 'express' (I've seen this before).
'apology?' becomes 'regret' (I can't explain this - if you can you should believe this answer much more).
'express'+'regret'='EXPRESS REGRET'

Can you help me to learn more?

I've seen this clue in The Telegraph.

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