Maynard, the son of former England batsman Matthew, began his career at Glamorgan before joining Surrey at the start of last season. He scored 2,384 runs at an average of almost 33 in his 48 first-class matches - with a top score of 143.
Thompson added: "Tom was a prodigiously talented young batsman who had made an incredible start to his career and was clearly destined for far greater things.
"The impact Tom made in such a short period of time for Surrey CCC spoke for itself. There is a profound sense of loss at the passing of Tom."
Clarke added: "This is a very sad day for everyone connected with Surrey County Cricket club and for Glamorgan County Cricket club where Tom spent the early part of his career."
A statement from Glamorgan CCC said they were "deeply saddened to hear of the tragic death of Tom Maynard" and the club's thoughts were with his family.
It added: "Most of our playing and coaching staff were close friends of Tom and understandably are still trying to come to terms with this sad news."
Former England captain Michael Vaughan:
"Thoughts are with Matt Maynard and his family. Words can't describe the terribly sad news that Tom Maynard has died aged 23... #RIPTOM"
Ex-England all-rounder Andrew Flintoff:
"Tragic news that a great lad, Tom Maynard, is no longer with us. All my thoughts are with his family at this awful time x x"
Former England seamer Matthew Hoggard:
"Can't believe the news about Tom Maynard !!!! Life can be so cruel! Thoughts go out to his family!! Top bloke much talent! R.I.P"
Durham all-rounder Paul Collingwood:
"The world has lost a true character that loved life and a hugely talented cricketer. My thoughts go out to the Maynard family. RIP Tom."
Former England bowler Darren Gough:
"Terrible news, Tom a fantastic athlete, great person who had so much to look forward too, I'm devastated for all that knew him."
BBC cricket correspondent Jonathan Agnew:
"How desperately sad. Heartfelt condolences to Matthew and family."
Managing director of England cricket Hugh Morris said Maynard was destined a career of high achievement.
"He had the world at his feet. I played with his old man when he played for England and Tom was very much on that pathway," he said.
"In many ways he was very similar to Matthew. He was an incredibly talented cricketer. He played for the Lions in the winter. He impressed all the coaches there.
"They liked him as a person and as a player and to have his life cut short in this way is an absolute tragedy."
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