Be divided by new term for hardliner (9)
I believe the answer is:
extremist
'hardliner' is the definition.
(someone with extreme views or policies)
'be divided by new term' is the wordplay.
'be' becomes 'exist' (synonyms).
'divided by' means one lot of letters goes inside another (inserted letters divide the word).
'new' indicates anagramming the letters.
'term' with letters rearranged gives 'trem'.
'exist' placed around 'trem' is 'EXTREMIST'.
'for' is the link.
(Other definitions for extremist that I've seen before include "An ultra-radical" , "One with highly non-standard views" , "One with views far from the mainstream" , "Views far beyond the norm" , "Ultra" .)