Second of concerts by celebrity, mainly for charity (5)
I believe the answer is:
oxfam
'for charity' is the definition.
(I've seen this before)
'second of concerts by celebrity mainly' is the wordplay.
'second of concerts' becomes 'o' (2nd letter of 'concerts').
'by' becomes 'x' (as in 'multiplied by').
'celebrity' becomes 'fame' (celebrity can mean the quality of being famous).
'mainly' means to remove the last letter (virtually or mainly the word, but not all of it).
'fame' with its final letter taken away is 'fam'.
'o'+'x'+'fam'='OXFAM'
(Other definitions for oxfam that I've seen before include "A famine-relief charity" , "Famine relief organisation" , "relief agency" , "Famine relief charity" , "Disaster-relief charity" .)