The answer is a TEAPOT or , TEACART
EXPLANATION
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The pronunciation off the letter T is 'tee'. We observe that 'tee' is a homophone of 'tea'.
Then, the given problem translates as:
"What starts with T, ends with T, and is full of tea"
Accordingly, the required word denotes a container full of tea.
This can only be a TEAPOT or, TEACART each of which starts and ends with Tea and, consequently is the answer to the given riddle.
Edited on June 28, 2022, 8:29 pm