Over time medic provided gear periodically for vagrant (7)
I believe the answer is:
drifter
'for vagrant' is the definition.
(synonyms)
'over time medic provided gear periodically' is the wordplay.
'over' says to put letters next to each other.
'time' becomes 't' (abbreviation).
'medic' becomes 'dr' (abbreviation for doctor).
'provided' becomes 'if' (eg 'provided it's sunny' means 'if it's sunny').
'periodically' indicates alternate letters (letters must be selected 'every so often').
The alternate letters of 'gear' are 'er'.
'dr'+'if'='drif'
't' after 'drif' is 'drift'.
'drift'+'er'='DRIFTER'
(Other definitions for drifter that I've seen before include "Bum" , "Fishing-boat" , "Wanderer; fishing vessel" , "Fishing boat; hobo" , "fellow lacking direction" .)