Resident in Mississippi, a not unerringly trained listener (5,5)
I believe the answer is:
piano tuner
'trained listener' is the definition.
(someone who listens to pitch)
'resident in mississippi a not unerringly' is the wordplay.
'resident' says the answer is hidden in the clue (I've seen 'resident of' mean this).
'PIANO TUNER' is hidden in the letters of 'in mississippi a not unerringly'.
(Other definitions for piano tuner that I've seen before include "Grand adjuster?" , "one with a fine ear?" , "Instrument adjuster" .)