Doctor in steeper improvement for thirty days (9)
I believe the answer is:
september
'thirty days' is the definition.
'doctor in steeper improvement' is the wordplay.
I cannot quite see how this works, but
'doctor' could be 'mb' (Bachelor of Medicine, Medicinae Baccalaureus) and 'mb' is present in the answer.
an anagram of 'steeper' is 'septeer' which is located in the left over letters.
No letters remain.
This explanation may well be incorrect...
'for' acts as a link.
Can you help me to learn more?
(Other definitions for september that I've seen before include "It follows 3" , "- Song (Kurt Weill)" , "The longest month?" , "Ninth month" , "Might tempers be altered this month?" .)