Promise shown by piano student on Fringe (6)
I believe the answer is:
pledge
'promise' is the definition.
(pledge is a kind of promise)
'piano student on fringe' is the wordplay.
'piano' becomes 'p' (musical abbreviation).
'student' becomes 'l' (as in L-plates for learner drivers).
'on' is a charade indicator (letters next to each other).
'fringe' becomes 'edge' (synonyms).
'p'+'l'+'edge'='PLEDGE'
'shown by' acts as a link.
(Other definitions for pledge that I've seen before include "assurance" , "Vow, affirm" , "Solemn undertaking" , "Promise, word of honour" , "Promise (to abstain?)" .)