Extra support to remain in place too long (8)

I believe the answer is:

overstay

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'remain in place too long' is the definition.
I can't judge whether this defines the answer.

'extra support' is the wordplay.
'extra' becomes 'over' (both can mean left over).
'support' becomes 'stay' (stay is a kind of support).
'over'+'stay'='OVERSTAY'

'to' is the link.

Can you help me to learn more?

(Other definitions for overstay that I've seen before include "Hang around too long" , "Remain too long" , "Linger too long" , "Leave too late" , "take advantage of hospitality?" .)

I've seen this clue in The Independent.

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