Listen to live between the start of October and the end of January (4)
I believe the answer is:
obey
'listen to' is the definition.
(I've seen this in another clue)
'live between the start of october and the end of january' is the wordplay.
'live' becomes 'be' (synonyms).
'between' indicates putting letters inside.
'the start of' indicates taking the first letters.
'and' means one lot of letters go next to another.
'the end of' says to take the final letters.
The initial letter of 'october' is 'o'.
The last letter of 'january' is 'y'.
'o'+'y'='oy'
'be' inserted into 'oy' is 'OBEY'.
(Other definitions for obey that I've seen before include "Carry out (an order)" , "Do what one is told" , "Submit to authority" , "Do as ordered" , "Accept instructions" .)