Father suggests it's up to me (4)
I believe the answer is:
time
'father' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'it's up to me' is the wordplay.
'up' is a reversal indicator (in down clue: letters go upwards).
'it' written backwards gives 'ti'.
'ti'+'me'='TIME'
'suggests' acts as a link.
Can you help me to learn more?
(Other definitions for time that I've seen before include "It's measured by watch or clock" , "See 12" , "Continuum of past, present and future" , "Procrastination is the thief of ." , "Rhythm" .)