The 19-year-old Zimbabwean was thrust into the left back position to replace the injured Leighton Baines and charmed Martinez with a fine display against newly-promoted Watford in the opening league match of the season at Goodson Park.
It was the Zimbabweanâ€™s second match, after he made his debut for the Merseyside club in a 2-1 win over West Ham in May 2015.
â€œI am impressed with the way Galloway along our other youth graduates, Tyias Browning and Mathew Pennington, are playing,â€ Martinez recently told the club’s website.
“Brendan Galloway is a young man, but when he plays, he is an out and out defender. He has been very impressive and is someone who can play in that position for us for a long time. He is destined for a successful career; I have no doubt about that.â€
Club captain Phil Jagielka also highlighted his liking for Galloway.
“Galloway is an impressive player with a lot of energy. He is coming in a position that we are probably a little bit light on as far as experience goes but we are more than happy with the standard of the lads coming through,â€ said Jagielka.
Galloway moved to England from Zimbabwe with his family when he was only six years old and started off playing for Milton Keynes Dons (MK Dons), when he joined the club’s under-11 side.
He became the youngest first team player in MK Dons’ history at 15 years of age, when he made his debut in a 6â€“0 victory at home to Nantwich Town in the FA cup in November 2011. The defender then made his league debut when he started for MK Dons in April 2012 against Rochdale.
He signed for Everton in August 2014 for an undisclosed fee, on a five-year contract.
Everton coach, Roberto Martinez, believes the clubâ€™s Zimbabwean-born defender, Brendan Zibusiso Galloway, is destined for greater heights.