Lady's outside, referring to musical instrument (4)
I believe the answer is:
lyre
'musical instrument' is the definition.
(lyre is a kind of musical instrument)
'lady's outside referring to' is the wordplay.
'outside' suggests removing the centre.
'referring to' becomes 're' ('re' means regarding or about).
'lady' with its centre removed is 'ly'.
'ly'+'re'='LYRE'
(Other definitions for lyre that I've seen before include "Old instrument, like a harp" , "Ancient harp-like instrument" , "Rely (anag.)" , "Ancient Greek stringed instrument" , "Old musical instrument with strings in U-shaped frame" .)