Had to follow medic getting overwhelmed (7)
I believe the answer is:
drowned
'overwhelmed' is the definition.
('drown' can be a synonym of 'overwhelm')
'had to follow medic' is the wordplay.
'had' becomes 'owned' ('own' can be a synonym of 'have').
'to follow' is a charade indicator (letters next to each other) (some letters go after or follow others).
'medic' becomes 'dr' (doctor).
'owned' put after 'dr' is 'DROWNED'.
'getting' acts as a link.
(Other definitions for drowned that I've seen before include "Submerged, flooded" , "Died underwater" , "Died by submersion" , "Lost at sea" , "Suffocated in water" .)