Sweet-talk student in having put on weight (7)
I believe the answer is:
flatter
'sweet-talk' is the definition.
(I've seen this in another clue)
'student in having put on weight' is the wordplay.
I cannot quite understand how this works, but
'student' could be 'l' (as in L-plates for learner drivers) and 'l' is present in the answer.
'on' could be 'at' (I've seen this in other clues) and 'at' is found within the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for flatter that I've seen before include "drier" , "Praise insincerely" , "Less hilly; show to advantage" , "Become" , "Lavish compliments on (someone)" .)