New Yorker’s to take out taxi, speeding around houses (4-3)

'new yorker's to' is the definition.
I can't tell whether this definition defines the answer.

'out taxi speeding around houses' is the wordplay.
'houses' indicates the answer is hidden within the clue (part of the clue houses the answer).
'around' says the letters should be written in reverse.
'xispeed' is hidden in the letters of 'out taxi speeding'.
'xispeed' backwards is 'DEEP-SIX'.

'take' is the link.

Can you help me to learn more?