Starts making on cooktop, having a coffee (5)
I believe the answer is:
mocha
'coffee' is the definition.
(mocha is a kind of coffee)
'starts making on cooktop having a' is the wordplay.
'starts' indicates taking the first letters.
The initial letters of 'making on cooktop having' is 'moch'.
'moch'+'a'='MOCHA'
(Other definitions for mocha that I've seen before include "Strong dark coffee" , "Coffee flavour" , "Fine-quality coffee" , "It may end up as grounds" , "Leather" .)