Start of second half of year, with a new way to describe calendar (6)
I believe the answer is:
julian
'way to describe calendar' is the definition.
(as in the Julian calendar)
'start of second half of year with a new' is the wordplay.
'start of second half of year' becomes 'Jul I' (July 1st).
'with' means one lot of letters go next to another.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'juli'+'a'+'n'='JULIAN'
(Other definitions for julian that I've seen before include "Sort of date" , "Calendar devised by Caesar" , "Associated with Caesar" , "boy" .)