Long period at the middle of the month (5)
I believe the answer is:
yearn
'long' is the definition.
(I know that long can be written as yearn)
'period at the middle of the month' is the wordplay.
'period' becomes 'year' (year is a kind of period).
'at' means one lot of letters go next to another.
'the middle of' indicates the central letters.
The central letter of 'month' is 'n'.
'year'+'n'='YEARN'
(Other definitions for yearn that I've seen before include "Have strong desire" , "Have a great longing" , "Long (for something)" , "Pant - pine" , "Desire, want" .)