Some like June and Maureen having short time in health organisation (6)
I believe the answer is:
months
'some like june' is the definition.
(months)
'maureen having short time in health organisation' is the wordplay.
'maureen' becomes 'mo' (I've seen this in other clues).
'having' says to put letters next to each other.
'short time' becomes 't' (abbreviation for time).
'in' means one lot of letters goes inside another.
'health organisation' becomes 'nhs' (National Health Service).
't' inserted into 'nhs' is 'nths'.
'mo'+'nths'='MONTHS'
'and' is the link.
(Other definitions for months that I've seen before include "Calendar divisions" , "17 and December" , "Divisions of time" , "Divisions of year" , "Periods of time" .)