Elizabeth welcoming second time by composer (5)
I believe the answer is:
liszt
'composer' is the definition.
(Franz Liszt)
'elizabeth welcoming second time' is the wordplay.
'elizabeth' becomes 'liz'.
'welcoming' indicates putting letters inside (in sense of 'inviting in').
'second' becomes 's' (common abbreviation).
'time' becomes 't'.
'liz' enclosing 's' is 'lisz'.
'lisz'+'t'='LISZT'
'by' is the link.
(Other definitions for liszt that I've seen before include "Hungarian virtuoso composer" , "Franz . . . . ., 19th century Hungarian composer and pianist" , "Famous composer" , "Hungarian piano virtuoso, d. 1886" , "Franz -, Hung. pianist" .)