Having a hearty appetite no good, getting very thin (5)
I believe the answer is:
reedy
'very thin' is the definition.
(I've seen this before)
'having a hearty appetite no good' is the wordplay.
'having a hearty appetite' becomes 'greedy'.
'no' indicates named letters should be taken away.
'good' becomes 'g' (abbreviation).
'greedy' with 'g' taken out is 'REEDY'.
'getting' is the link.
(Other definitions for reedy that I've seen before include "edge of some river-banks" , "Thin and piping" , "(Of a person) tall and thin" , "Piping, fluting" , "Like some of the wind" .)