Doctor in Leith arranged protective cover for finger (7)
I believe the answer is:
thimble
'protective cover for finger' is the definition.
'doctor in leith arranged' is the wordplay.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'in' means one lot of letters goes inside another.
'arranged' indicates an anagram.
'leith' is an anagram of 'thile'.
'mb' inserted within 'thile' is 'THIMBLE'.
(Other definitions for thimble that I've seen before include "See 5" , "Sewer's aid" , "one player conceals in game" , "Protection for part of arm" , "digital screen" .)