Navy follows method to get contemporary (6)
I believe the answer is:
modern
'contemporary' is the definition.
(similar in meaning)
'navy follows method' is the wordplay.
'navy' becomes 'RN' (abbreviation for Royal Navy).
'follows' means one lot of letters go next to another.
'method' becomes 'mode' (way of doing something).
'rn' after 'mode' is 'MODERN'.
'to get' is the link.
(Other definitions for modern that I've seen before include "Present-day" , "In history, the period or era since the Middle Ages" , "Novel" , "The very latest available" , "Of the present time or current fashion" .)