Tire out former partner with headgear going round America (7)
I believe the answer is:
exhaust
'tire out' is the definition.
(exhausting is a kind of tiring out)
'former partner with headgear going round america' is the wordplay.
'former partner' becomes 'ex' (an ex-partner).
'with' means one lot of letters go next to another.
'headgear' becomes 'hat' (hats are a type of headgear).
'going round' is an insertion indicator (some letters go around others).
'america' becomes 'US' (United States).
'hat' enclosing 'us' is 'haust'.
'ex'+'haust'='EXHAUST'
(Other definitions for exhaust that I've seen before include "Empty" , "Tube carrying off fumes from car engine" , "Sap - piped emission" , "Car's waste gas" , "Wear, tire out" .)