Not one check over migrant (5)
I believe the answer is:
nomad
'migrant' is the definition.
(someone who travels around)
'not one check over' is the wordplay.
'not' becomes 'no' (I've seen this in other clues).
'one check' becomes 'dam' (dam can mean to check or restrict water).
'over' is a reversal indicator.
'dam' reversed gives 'mad'.
'no'+'mad'='NOMAD'
(Other definitions for nomad that I've seen before include "Person always on the move" , "Itinerant" , "Member of travelling people" , "wandering type" , "A wandering tribesman" .)