Without coordination, a cab's beginning to circle another (6)

'without coordination' is the definition.
(ataxia affects bodily coordination)

'a cab's beginning to circle another' is the wordplay.
'beginning' says to take the initial letters.
'to circle' indicates putting letters inside.
'another' becomes 'taxi' (I can't justify this - if you can you should give a lot more credence to this answer).
The initial letter of 'cabs' is 'c'.
'a'+'c'='ac'
'ac' enclosing 'taxi' is 'ATAXIC'.