Nurture offered by wet doctor over time (9)

'nurture' is the definition.
(I know that breeding can be written as fosterage)

'wet doctor over time' is the wordplay.
'wet doctor' becomes 'Foster' (as in the nursery rhyme character Doctor Foster).
'over' means one lot of letters go next to another.
'time' becomes 'age' (an age is a period of time).
'foster'+'age'='FOSTERAGE'

'offered by' is the link.