Lyre hard to play — that business with the arms? (8)
I believe the answer is:
heraldry
'the arms?' is the definition.
(arms is a kind of heraldry)
'lyre hard to play' is the wordplay.
'to play' indicates an anagram.
'lyre'+'hard'='lyrehard'
'lyrehard' anagrammed gives 'HERALDRY'.
'that business with' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for heraldry that I've seen before include "Classification of armorial bearings" , "Armorial bearings, insignia etc" , "System of coats of arms and the like" , "Study of coats of arms etc" , "The study of crests and genealogies" .)