Long piano in conservatoire at last (4)
I believe the answer is:
pine
'long' is the definition.
(to pine for someone is to long for them)
'piano in conservatoire at last' is the wordplay.
'piano' becomes 'p' (musical abbreviation).
'at last' suggests the final letters.
The final letter of 'conservatoire' is 'e'.
'p'+'in'+'e'='PINE'
(Other definitions for pine that I've seen before include "Coniferous tree" , "Kind of needle" , "Thirst" , "Scots fir" , "Long for the conifer?" .)