Crossword Genius

Lose the head, hover, don't budge and wear out welcome (8)

Ross

I believe the answer is:

overstay

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

'lose' is the definition.
Although both the answer and definition are verbs in their base form, I cannot see how they can define each other.

'head hover don't budge and wear out welcome' is the wordplay.
I cannot quite understand how this works, but
'don't budge' could be 'stay' (I've seen this in another clue) and 'stay' is present in the answer.
The remaining letters 'over' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'the' is the link.

Can you help me to learn more?

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

I've seen this clue in The Irish Times.
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