Initially, applicant with medical degree on day left a covering letter (6)
'covering letter' is the definition.
Both the answer and definition are singular nouns.
Maybe there's an association between them I don't understand?
'initially applicant with medical degree on day left a' is the wordplay.
'initially' indicates taking the first letters.
'with' is a charade indicator (letters next to each other).
'medical degree' becomes 'MB' (Bachelor of Medicine).
'on' indicates putting letters inside (as in clothing 'on' a person).
'day left' becomes 'oe' (I can't justify this - if you can you should give a lot more credence to this answer).
The initial letter of 'applicant' is 'a'.
'mb' going around 'oe' is 'moeb'.
'a'+'moeb'+'a'='AMOEBA'
(Other definitions for amoeba that I've seen before include "cell for life" , "shape-shifter" , "Water protozoan" , "Simplest animal form" , "Microscopic organism consisting of a single cell changing constantly" .)
'a covering letter' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.
'initially applicant with medical degree on day left' is the wordplay.
'initially' indicates taking the first letters.
'with' says to put letters next to each other.
'medical degree' becomes 'MB' (Bachelor of Medicine).
'on' means one lot of letters goes inside another.
'day left' becomes 'cot' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The first letter of 'applicant' is 'a'.
'a' after 'mb' is 'mba'.
'mba' put into 'cot' is 'COMBAT'.
(Other definitions for combat that I've seen before include "Fight against; fighting" , "War; contest" , "Battle or fight" , "A fight or contest, sometimes mortal" , "Take action to deal with - fight" .)
'letter' is the definition.
(letter of the Greek alphabet)
'initially applicant with medical degree on day left a covering' is the wordplay.
'initially' says to take the initial letters.
'with' is an insertion indicator.
'medical degree' becomes 'MB' (Bachelor of Medicine).
'on day left' becomes 'lad' (I can't justify this - if you can you should believe this answer much more).
'a covering' is a charade indicator (letters next to each other) (on top of in down clue).
The initial letter of 'applicant' is 'a'.
'mb' inserted inside 'lad' is 'lambd'.
'a' put after 'lambd' is 'LAMBDA'.
(Other definitions for lambda that I've seen before include "character from Greece" , "Foreign character" , "Greek letter - am bald (anag)" , "part of the skull" , "Eleventh Greek letter" .)