Heartily, she gives Jane a bit of a smile (7)
I believe the answer is:
jasmine
'bit of a smile' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'heartily she gives jane a' is the wordplay.
I cannot quite understand how this works, but
'she' could be 'jasmin' and 'jasmin' is present in the answer.
A single letter 'e' remains which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for jasmine that I've seen before include "Fragrant flower" , "Shrub with fragrant yellow or white flowers" , "Fragrant shrub used to flavour tea" , "Plant" , "Sweet-smelling shrub" .)