Piano tuner's first to leave punctually for concert (4)
I believe the answer is:
prom
'concert' is the definition.
(abbreviation for promenade concert)
'piano tuner's first to leave punctually' is the wordplay.
'piano tuner's first' becomes 'rom' (I can't justify this - if you can you should give a lot more credence to this answer).
'to' means one lot of letters go next to another (I've seen this in other clues).
'leave' says to take the initial letters (I've seen 'left of' mean this (the leftmost letter in the word)).
The initial letter of 'punctually' is 'p'.
'rom' after 'p' is 'PROM'.
'for' is the link.
(Other definitions for prom that I've seen before include "hop" , "Albert Hall concert" , "Walkway; concert" , "Formal dance at the end of school year" , "Esplanade" .)