Need time after Spare, Prince Harry ultimately admits (7)

I believe the answer is:

poverty

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

'need time' is the definition.
'poverty' can be an answer for 'need' (I've seen this before). I'm unsure of the 'time' bit.

'spare prince harry ultimately admits' is the wordplay.
'spare' becomes 'overt' (I can't justify this - if you can you should give a lot more credence to this answer).
'prince' becomes 'p' (abbreviation for prince).
'ultimately' suggests the final letters.
'admits' indicates putting letters inside.
The last letter of 'harry' is 'y'.
'p'+'y'='py'
'overt' going inside 'py' is 'POVERTY'.

'after' is the link.

Can you help me to learn more?

(Other definitions for poverty that I've seen before include "'When ....... comes in at the door, love flies out of the window'" , "Poor state" , "Indigence" , "Need" , "Lack of money etc" .)

I've seen this clue in The Guardian.

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