Live carefully, supporting daughter (5)
I believe the answer is:
dwell
'live' is the definition.
(synonyms)
'carefully supporting daughter' is the wordplay.
'carefully' becomes 'well' (doing something well can mean doing it carefully).
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'daughter' becomes 'd' (genealogical abbreviation).
'well' put after 'd' is 'DWELL'.
(Other definitions for dwell that I've seen before include "Exist (within)" , "Abide, reside" , "Hang out" , "Reside - linger" , "Think moodily (on something)" .)