Persevere at an old composition for the piano (4)
I believe the answer is:
plod
'persevere' is the definition.
(I've seen this in another clue)
'an old composition for the piano' is the wordplay.
'composition' is an anagram indicator.
'for' is a charade indicator (letters next to each other) (I've seen this in other clues).
'the piano' becomes 'p' (musical abbreviation).
'old' with letters rearranged gives 'lod'.
'lod' after 'p' is 'PLOD'.
'at' is the link.
(Other definitions for plod that I've seen before include "Shamus, say" , "Work painstakingly" , "Heavy walk; PC (slang)" , "Walk with heavy steps" , "Copper" .)