Tavernier penned a new contract with Rangers on Tuesday, that saw him extend his stay at Ibrox until the summer of 2024.
The Rangers captain was pivotal in the Gers’ Scottish Premiership triumph this season with his tally of eleven goals and ten assists in 29 league appearances.
After signing a new contract with the Gers, the 29-year-old revealed his ambition to win the Scottish Cup among other trophies as Tavernier stated that he still has unfinished business at Rangers.
Tavernier went on to express his desire to add to Rangers’ trophy cabinet and extend their run of success as the English full-back looks forward towards meeting new challenges.
“This is only the start of something really special for this club from where we are at now. It is not the end, it is the start of something”, Tavernier told Rangers’ official site.
“I cannot wait. On May 15, it will really set in what we have achieved and hopefully we can have some fans in the stadium so they can enjoy it with us.
“But you have that little taste of success and you just want more and more and we have the Scottish Cup, and we are in that to win that.
“You just want to constantly win more and more trophies and it was an easy decision when the club offered me an extension.
“I still have unfinished business – there are cups there that I haven’t won that I want to win, so I am looking to stay.”
After beating Celtic to the Scottish Premiership title this season, Tavernier will look to help Rangers knock out the Hoops when the two teams meet in a Scottish Cup fourth round tie on 17th April.