The 23-year-old, who made his first-class debut in 2015, will now remain at Trent Bridge until the end of the 2021 campaign.
Carter impressed during this summer’s Vitality Blast, taking 14 wickets as the Outlaws reached Finals Day.
“There’s no better place for me to develop my game than at Trent Bridge with Notts,” he told the club website.
“With promotion to aim for in the Championship – and also for our white-ball side to achieve what it’s capable of by winning a trophy – there’s loads for us to achieve here in 2020 and beyond.”
Nottinghamshire head coach Peter Moores said: “Matt is proving himself to be a really exciting player.
“He became a trusted, go to bowler for us last summer and he earned that trust from his captain on merit with his performances.”
The former West Indies batsman died aged 95 on Wednesday.
Third test against West Indies will be dedicated to raising money.
The Barbados Cricket Association president wanted the Windies head coach sacked after he went to his father-in-law’s funeral.
Holder did not bowl in the first internal warm-up match last week amid doubts over an ankle niggle.
The Gloucestershire wicketkeeper-batsman top-scored with a hard-earned 85 for Jos Buttler’s side.
Weekes scored scored 4,455 runs in 48 Tests and received his knighthood in 1995.
The Windies could call on Da Silva for the first Test against England following his display in this warm-up match.
It was ‘Team Stokes’ against ‘Team Buttler’ at the Ageas Bowl.