Recovered from vaccination? Went too far (8)
I believe the answer is:
overshot
'went too far' is the definition.
(I've seen this in another clue)
'recovered from vaccination?' is the wordplay.
'recovered from' becomes 'over' (as in being over an illness).
'vaccination?' becomes 'shot' (shot can mean a vaccination).
'over'+'shot'='OVERSHOT'
(Other definitions for overshot that I've seen before include "Passed beyond the mark or runway" , "was pitched wrong?" , "needed to pull back?" , "Went past the target" , "Went beyond the mark" .)