Persevere with a new motto (6)
I believe the answer is:
slogan
'motto' is the definition.
(I know that motto can be written as slogan)
'persevere with a new' is the wordplay.
'persevere' becomes 'slog' (slog can mean to carry on or persevere).
'with' means one lot of letters go next to another.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'slog'+'a'+'n'='SLOGAN'
(Other definitions for slogan that I've seen before include "'Motto, watchword (6)'" , "advertising catch phrase" , "Ad. catchphrase" , "Tag line" , "Short catchy phrase used in advertising" .)