And with the very strong possibility of winning full international recognition just a few weeks away, Vesty is also hoping to finish the club season on a high by helping Tigers complete a sensational double in Scotland on Saturday.
The Tigers face Leinster in the Heineken Cup final at Murrayfield but Vesty says they must play better than they did against London Irish at Twickenham on Saturday.
"Last week we didn't play well but ended up gutsing out a tough win out but that's the sign of a good team as well," he said.
"To come out of the season with two cups under our belt would be astonishing.
"I have never won the Heineken Cup and I certainly really want it. To win the Premiership was brilliant but it feels like there is another job to do."
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