Solo arranged by an egghead for free (5)
I believe the answer is:
loose
'free' is the definition.
('loose' can be similar in meaning to 'free')
'solo arranged by an egghead' is the wordplay.
'arranged' indicates anagramming the letters.
'by' says to put letters next to each other.
'an egghead' becomes 'e' (head letter of 'egg').
'solo' anagrammed gives 'loos'.
'loos'+'e'='LOOSE'
'for' is the link.
(Other definitions for loose that I've seen before include "Free or immoral" , "released from confinement" , "Not tied up or attached" , "Untie(d)" , "Freed" .)