The most common and most likely answer to this crossword clue is the 5 letter word TODDY
I've seen this crossword clue in The Guardian
T
O
D
D
Y
More clues leading to the result TODDY
- Extremely tipsy drinking rum, an alcoholic beverage
- Now daughter comes in for a hot drink
- Get extremely tiddly, imbibing rum in this?
- It could make one extremely tiddly with rum in it
- Drink rum in Torquay, empty
- Sweet hot drink for rum type avoiding exercise outside
- Sycophant undergoes change of heart but provides hot drink
- Drink rum in case of tragedy
- Rattle by imbibing doubledĀ drinkĀ
- Cobb swallows strange hot drink
Buddy explains!

The straight part
We know that "It could make one extremely tiddly with rum in it" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it could make one extremely tiddly with rum in it = toddy.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does TODDY mean?
TODDY noun- A drink made from alcoholic liquor mixed with sugar, spice and hot water.
- The sweet sap from any of several tropical trees fermented to make an alcoholic drink.