Month ending with out-of-this world group performing (5)
I believe the answer is:
octet
'group performing' is the definition.
(group of eight musicians)
'month ending with out-of-this world' is the wordplay.
'month' becomes 'oct' (Oct is an example).
'ending with' says to put letters next to each other.
'out-of-this world' becomes 'et' (abbreviation for extraterrestrial).
'oct'+'et'='OCTET'
(Other definitions for octet that I've seen before include "Eight people together" , "Chamber ensemble, a Mendelssohn favourite" , "Composition for eight musicians" , "A number of musicians" , "Group that plays" .)