Daughter running up to give assent (3)
I believe the answer is:
nod
'give assent' is the definition.
(I've seen this in another clue)
'daughter running up' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'running' becomes 'on' (eg when a machine is running it is on).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'd'+'on'='don'
'don' written backwards gives 'NOD'.
'to' acts as a link.
(Other definitions for nod that I've seen before include "What Homer may sometime do" , "OK" , "Sign of agreement" , "Indicate agreement (or sleepiness!)" , "drift" .)