The English-speaker has to leave without the band (6)
I believe the answer is:
gringo
'the english-speaker has' is the definition.
I can't judge whether this definition defines the answer.
'leave without the band' is the wordplay.
'leave' becomes 'go' (to go is to depart or leave).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'the band' becomes 'ring' (a ring is a band of metal).
'go' going around 'ring' is 'GRINGO'.
'to' is the link.
Can you help me to learn more?
(Other definitions for gringo that I've seen before include "English-speaker abroad" , "Latin-American term for English speaker" , "What the Mexican calls the American" , "Non-Spanish speaker" .)