Santa Fe charms artist travelling astride horse (6,9)
I believe the answer is:
father christmas
'santa' is the definition.
(I know that santa can be written as Father Christmas)
'fe charms artist travelling astride horse' is the wordplay.
'travelling' indicates an anagram.
'astride' means one lot of letters goes inside another.
'horse' becomes 'H' (abbreviation as in horse power).
'fe'+'charms'+'artist'='fecharmsartist'
'fecharmsartist' anagrammed gives 'fathercristmas'.
'fathercristmas' enclosing 'h' is 'FATHER CHRISTMAS'.
(Other definitions for father christmas that I've seen before include "present supremo" , "man with gifts" , "he'll be sacked" , "Santa!" , "late December he's busy" .)