A burning romance somehow holds it up (9)
I believe the answer is:
cremation
'a burning' is the definition.
(burning of a body)
'romance somehow holds it up' is the wordplay.
'somehow' is an anagram indicator.
'holds' means one lot of letters goes inside another.
'up' is a reversal indicator (in down clue: letters go upwards).
'it' in reverse letter order is 'ti'.
'romance' with letters rearranged gives 'cremaon'.
'cremaon' placed around 'ti' is 'CREMATION'.
(Other definitions for cremation that I've seen before include "The burning of a body" , "The incineration of a dead body" .)