Tending to race up and burst into song (7)
I believe the answer is:
nursing
'tending' is the definition.
(nurses tend to patients)
'race up and burst into song' is the wordplay.
'race' becomes 'run' (run is a kind of race).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'and' means one lot of letters go next to another.
'burst into song' becomes 'sing'.
'run' backwards is 'nur'.
'nur'+'sing'='NURSING'
'to' acts as a link.
(Other definitions for nursing that I've seen before include "sister's career" , "Patient care" , "Feeding baby" , "Medical vocation" , "now a graduate profession" .)