Walk extremely eager having to spat (6)
I believe the answer is:
gaiter
'to spat' is the definition.
('gaiter' can be a synonym of 'spat')
'walk extremely eager' is the wordplay.
'walk' becomes 'gait' (gait is a kind of walk).
'extremely' means to remove the middle letters.
'eager' with its centre taken out is 'er'.
'gait'+'er'='GAITER'
'having' is the link.
(Other definitions for gaiter that I've seen before include "Leg cover, spat" , "Legging to cover ankle and instep" , "Ankle and lower leg cover" , "Legging or spat" , "Lower leg covering" .)